**robertogreco : geometry**
54

MuirMcNeil's New Typeface Is As Fragmented and Malleable As Memory | | Eye on Design

august 2018 by robertogreco

"Name: Bisect

Designer: Natasha Lucas in collaboration with MuirMcNeil

Foundry: MuirMcNeil

Release Date: July 2018

Back Story: While still a student at the London College of Communication, graphic designer Natasha Lucas began designing Bisect as a part of a larger project based on Harold Pinter’s mid-career “memory plays.” In a memory play, a lead character narrates events drawn from memories that may or may not be factually accurate. Pinter’s Old Times (1971), No Man’s Land (1975), and Betrayal (1978) question how faulty memory and false perception lead us to harmful conclusions and personal betrayals.

Lucas developed the Bisect type system as a visual expression of the progressive fragmentation of language as it erodes through the selective, faulty nature of memory. At the same time, she wanted to create a coherent visual type system that would work across a range of print and digital media. She developed a subtly modulated grid for the construction of Bisect’s letterforms, governed by a playful exchange between separate segments. Subsequently, MuirMcNeil developed a full character set and cut Bisect in three versions.

Why’s it called Bisect? The word bisect means “to divide into two usually equal parts,” and this typeface does just that with its letterforms, carving each one into vertical and horizontal segments that register precisely with one another in layers to offer a wide range of visual possibilities.

What are its distinguishing characteristics? Bisect is a monospaced geometric type system, and all its letters occupy squares. The designer constructed the letterforms using a meticulous, subtle relationship of vertical, horizontal, and curved segments along with extremely tight letter spacing. The characters look as if they’re formed from Modernist ribbons, with well-deployed uses of negative space; the P, for instance, does not have a completed stroke for its spine and verges on the abstract, yet somehow maintains its integrity and legibility as a letter. Bisect is available in Opentype encoding for Macintosh.

What should I use it for? Just ask Paul McNeil, partner in the foundry bearing his name: “Big settings/strong settings/short settings/brand identity designs/posters/typographic animations/play/fun/exploration.”

What other typefaces do you like to pair it with? “We don’t. The notion of ‘font pairing’ brings us out in a rash—but Bisect contrasts well with just about anything,” says McNeil. Skin ailments aside, geometric sans serifs such as London are logical companions thanks to their visually obvious mathematical roots. "

fonts
typography
muirmcneil
2018
srg
language
natashalucas
memory
malleability
fragmentation
geometry
Designer: Natasha Lucas in collaboration with MuirMcNeil

Foundry: MuirMcNeil

Release Date: July 2018

Back Story: While still a student at the London College of Communication, graphic designer Natasha Lucas began designing Bisect as a part of a larger project based on Harold Pinter’s mid-career “memory plays.” In a memory play, a lead character narrates events drawn from memories that may or may not be factually accurate. Pinter’s Old Times (1971), No Man’s Land (1975), and Betrayal (1978) question how faulty memory and false perception lead us to harmful conclusions and personal betrayals.

Lucas developed the Bisect type system as a visual expression of the progressive fragmentation of language as it erodes through the selective, faulty nature of memory. At the same time, she wanted to create a coherent visual type system that would work across a range of print and digital media. She developed a subtly modulated grid for the construction of Bisect’s letterforms, governed by a playful exchange between separate segments. Subsequently, MuirMcNeil developed a full character set and cut Bisect in three versions.

Why’s it called Bisect? The word bisect means “to divide into two usually equal parts,” and this typeface does just that with its letterforms, carving each one into vertical and horizontal segments that register precisely with one another in layers to offer a wide range of visual possibilities.

What are its distinguishing characteristics? Bisect is a monospaced geometric type system, and all its letters occupy squares. The designer constructed the letterforms using a meticulous, subtle relationship of vertical, horizontal, and curved segments along with extremely tight letter spacing. The characters look as if they’re formed from Modernist ribbons, with well-deployed uses of negative space; the P, for instance, does not have a completed stroke for its spine and verges on the abstract, yet somehow maintains its integrity and legibility as a letter. Bisect is available in Opentype encoding for Macintosh.

What should I use it for? Just ask Paul McNeil, partner in the foundry bearing his name: “Big settings/strong settings/short settings/brand identity designs/posters/typographic animations/play/fun/exploration.”

What other typefaces do you like to pair it with? “We don’t. The notion of ‘font pairing’ brings us out in a rash—but Bisect contrasts well with just about anything,” says McNeil. Skin ailments aside, geometric sans serifs such as London are logical companions thanks to their visually obvious mathematical roots. "

august 2018 by robertogreco

Rabbit Ear, origami and creative code

june 2018 by robertogreco

"Rabbit Ear is a creative coding javascript library for designing origami."

[See also: https://origami.pw/docs/ ]

software
origami
folding
classideas
foreden
computation
geometry
javascript
programming
[See also: https://origami.pw/docs/ ]

june 2018 by robertogreco

Combinatorics and Higher Dimensions - Numberphile - YouTube

april 2018 by robertogreco

"Featuring Federico Ardila from San Francisco State University - filmed at MSRI.

More links & stuff in full description below ↓↓↓

Federico previously on Numberphile ["Looking at Perfect Shuffles"]: https://www.youtu.be/OfEv5ZdSrhY

Federico's webpage: http://math.sfsu.edu/federico/

Antarctica Timelapse: https://www.youtu.be/o71TFQBTCG0

Objectivity: https://www.youtube.com/c/objectivity_videos "

federicoardila
math
mathematics
combinatorics
geometry
classideas
geometriccombinatorics
More links & stuff in full description below ↓↓↓

Federico previously on Numberphile ["Looking at Perfect Shuffles"]: https://www.youtu.be/OfEv5ZdSrhY

Federico's webpage: http://math.sfsu.edu/federico/

Antarctica Timelapse: https://www.youtu.be/o71TFQBTCG0

Objectivity: https://www.youtube.com/c/objectivity_videos "

april 2018 by robertogreco

Paper Models of Polyhedra

january 2017 by robertogreco

"Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia. On this site are a few hundred paper models available for free.

Make the models yourself.

Click on a picture to go to a page with a net of the model."

papercraft
via:dvsch
math
mathematics
geometry
art
classideas
polyhedra
Make the models yourself.

Click on a picture to go to a page with a net of the model."

january 2017 by robertogreco

Turtle

july 2016 by robertogreco

"A Library by Leah Buechley for the Processing programming environment. The Turtle library provides an implementation of a LOGO Turtle for Processing.

Turtle Geometry (see the fabulous book of the same name by Hal Abelson and Andrea diSessa) provides a different way of thinking about geometry. You draw by driving around a "turtle". Programs are written from the point of view of this turtle, which enables you to take an embodied approach to geometry.

LOGO, a turtle-based programming language, was developed by Seymour Papert and a group of collaboraters in the late 1960s. It was presented as a novel way to introduce children to computer programming and mathematics. LOGO and Turtle Geometry remain strongly associated with children and education, but are full of beautiful tools and ideas that adult artists and programmers can fruitfully explore.

A previous turtle library for Processing, Terrapin, is great, but somewhat limited in functionality. This library provides a more full-featured implementation, including "push" and "pop" functionality as well as high-resolution drawing capabilities.

DOWNLOAD

Download Turtle version 1.0.0 (1) in .zip format."

leahbuechley
logo
processing
programming
geometry
2016
Turtle Geometry (see the fabulous book of the same name by Hal Abelson and Andrea diSessa) provides a different way of thinking about geometry. You draw by driving around a "turtle". Programs are written from the point of view of this turtle, which enables you to take an embodied approach to geometry.

LOGO, a turtle-based programming language, was developed by Seymour Papert and a group of collaboraters in the late 1960s. It was presented as a novel way to introduce children to computer programming and mathematics. LOGO and Turtle Geometry remain strongly associated with children and education, but are full of beautiful tools and ideas that adult artists and programmers can fruitfully explore.

A previous turtle library for Processing, Terrapin, is great, but somewhat limited in functionality. This library provides a more full-featured implementation, including "push" and "pop" functionality as well as high-resolution drawing capabilities.

DOWNLOAD

Download Turtle version 1.0.0 (1) in .zip format."

july 2016 by robertogreco

When I Let Them Own the Problem

april 2016 by robertogreco

"There is essentially nothing left in this problem for students to explore and figure out on their own. If anything, all those labels with numbers and variables conspire to turn kids off to math. Ironically even when the problem tells kids what to do (use similar triangles), the first thing kids say when they see a problem like this is, “I don’t get it.”

They say they don’t get it because they never got to own the problem.

I wiped out the entire question and gave each student this mostly blank piece of paper and the following verbal instructions:"

…

"This lesson leaves me so full and proud. Their singing to the Stones while struggling in math makes me crazy in love with them."

math
teaching
mathematics
education
classideas
2013
geometry
They say they don’t get it because they never got to own the problem.

I wiped out the entire question and gave each student this mostly blank piece of paper and the following verbal instructions:"

…

"This lesson leaves me so full and proud. Their singing to the Stones while struggling in math makes me crazy in love with them."

april 2016 by robertogreco

Engare

march 2016 by robertogreco

"Engare is a game about movement and geometry."

[See also: https://www.youtube.com/watch?v=q3GqwTEP9yo ]

[also on Steam: http://store.steampowered.com/app/415170/Engare/ ]

software
drawing
mac
osx
applications
windows
ios
edg
srg
games
gaming
geometry
math
mathematics
[See also: https://www.youtube.com/watch?v=q3GqwTEP9yo ]

[also on Steam: http://store.steampowered.com/app/415170/Engare/ ]

march 2016 by robertogreco

Mooooooving — Animated GIFs by Guy Moorhouse

october 2015 by robertogreco

"Mooooooving is a side project featuring animated gifs I make using Processing and Flash.

My one rule is that the animations must start and end on a blank white frame — I kind of like the idea that they come out of nothing and return to nothing.

Anyway, hope you like them."

[via: http://interconnected.org/home/2015/10/05/filtered ]

tumblrs
motion
geometry
design
animation
guymoorhouse
gifs
processing
flash
coding
My one rule is that the animations must start and end on a blank white frame — I kind of like the idea that they come out of nothing and return to nothing.

Anyway, hope you like them."

[via: http://interconnected.org/home/2015/10/05/filtered ]

october 2015 by robertogreco

Broug Ateliers: Islamic Geometric Design

january 2015 by robertogreco

"Geometrical design is one of the most distinctive aspects of Islamic art and architecture. Geometry can be seen everywhere in the Islamic world: on buildings, in books, on tiles, on wood, on metal. This website celebrates the diversity of Islamic geometrical designs as well as demonstrating how traditional craftsmen make their designs.

Anyone can learn how to create Islamic geometric designs. It does not require an aptitude or even enthusiasm for mathematics or geometry. Understanding how geometrical designs are constructed gives an artist the tools and insights that are needed to create geometrical designs. So, if you can understand how a design was made, you can put yourself in the shoes of the traditional craftsman and learn how to create designs in the way it has been done for centuries.

All that is required is the ability to draw circles and straight lines. Traditional Islamic geometrical design is based on connecting intersections between circles and lines. This website offers an extensive 'educational' section on the practical aspects of traditional design."

art
islam
architecture
design
geometry
ericbroug
patterns
Anyone can learn how to create Islamic geometric designs. It does not require an aptitude or even enthusiasm for mathematics or geometry. Understanding how geometrical designs are constructed gives an artist the tools and insights that are needed to create geometrical designs. So, if you can understand how a design was made, you can put yourself in the shoes of the traditional craftsman and learn how to create designs in the way it has been done for centuries.

All that is required is the ability to draw circles and straight lines. Traditional Islamic geometrical design is based on connecting intersections between circles and lines. This website offers an extensive 'educational' section on the practical aspects of traditional design."

january 2015 by robertogreco

Building a better shapes book | Talking Math with Your Kids

january 2015 by robertogreco

"There are many shapes books available for reading with children. Most of them are very bad. I have complained about this for years.

Now I have done something about it.

Most shapes books—whether board books for babies and toddlers, or more sophisticated books for school-aged children—are full of misinformation and missed opportunities. As an example, there is nearly always one page for squares and a separate one for rectangles. There is almost never a square on the rectangles page. That’s a missed opportunity. Often, the text says that a rectangle has two short sides and two long sides. That’s misinformation. A square is a special rectangle, just as a child is a special person.

After years of contemplation, I had a kernel of an idea the other night. The kids are back in school before I am, so I had some flex time available. One thing led to another and voilá. I give you a better shapes book.

Download the pdf by clicking this link.

HOW TO USE THIS BOOK

On every page are four shapes. The question is the same throughout the book—which one doesn’t belong?

For example, which shape doesn’t belong in this set?

[image]

If you are thinking, “It depends on how you look at it,” then you’ve got the idea.

• The bottom left shape doesn’t belong because it’s not shaded in.

• The top left shape doesn’t belong because it only has three sides, while the others have four.

• The top right doesn’t belong because it is the only square.

• The bottom right doesn’t belong because it’s the only one resting on a side.

• Maybe you have different reasons for some of these. That’s great! The only measure of being right is whether your reason is true.

With an infant, you can use this book like any other shapes book. Look at each page together. Point at each shape and talk about it as you snuggle.

With a young child, ask which one doesn’t belong and why. Most pages in the book have at least one shape that a young child can identify as not belonging. Join the conversation by pointing out a different shape that doesn’t belong for some other reason.

With an older child, challenge yourselves to find a reason for each of the 44 shapes in the book.

There is no answer key. This is intentional–to encourage further discussion, and to encourage you to return to the book to try again. I have tested the file out on the Kindle app on my iPad, and it looks good. I made one printed copy and prefer it to the e-version because I can leave it out for browsing and we can touch the shapes without accidentally turning the page.

THE LEGAL DETAILS

You are free to download, share and use the pdf file. You are free to print it out until I make hard copies available for sale, which will likely be sometime this spring.

You are not free to sell it in any form.

Enjoy and report back, won’t you?

I owe thanks to Terry Wyberg at the University of Minnesota, who regularly plays the “Which one doesn’t belong?” game with numbers in professional development sessions, and to my online colleagues including but limited to Justin Lanier, Megan Schmidt, Dave Peterson, Matt Enlow and Andy Rundquist.

books
shapes
geometry
math
children
conversation
christopherdanielson
Now I have done something about it.

Most shapes books—whether board books for babies and toddlers, or more sophisticated books for school-aged children—are full of misinformation and missed opportunities. As an example, there is nearly always one page for squares and a separate one for rectangles. There is almost never a square on the rectangles page. That’s a missed opportunity. Often, the text says that a rectangle has two short sides and two long sides. That’s misinformation. A square is a special rectangle, just as a child is a special person.

After years of contemplation, I had a kernel of an idea the other night. The kids are back in school before I am, so I had some flex time available. One thing led to another and voilá. I give you a better shapes book.

Download the pdf by clicking this link.

HOW TO USE THIS BOOK

On every page are four shapes. The question is the same throughout the book—which one doesn’t belong?

For example, which shape doesn’t belong in this set?

[image]

If you are thinking, “It depends on how you look at it,” then you’ve got the idea.

• The bottom left shape doesn’t belong because it’s not shaded in.

• The top left shape doesn’t belong because it only has three sides, while the others have four.

• The top right doesn’t belong because it is the only square.

• The bottom right doesn’t belong because it’s the only one resting on a side.

• Maybe you have different reasons for some of these. That’s great! The only measure of being right is whether your reason is true.

With an infant, you can use this book like any other shapes book. Look at each page together. Point at each shape and talk about it as you snuggle.

With a young child, ask which one doesn’t belong and why. Most pages in the book have at least one shape that a young child can identify as not belonging. Join the conversation by pointing out a different shape that doesn’t belong for some other reason.

With an older child, challenge yourselves to find a reason for each of the 44 shapes in the book.

There is no answer key. This is intentional–to encourage further discussion, and to encourage you to return to the book to try again. I have tested the file out on the Kindle app on my iPad, and it looks good. I made one printed copy and prefer it to the e-version because I can leave it out for browsing and we can touch the shapes without accidentally turning the page.

THE LEGAL DETAILS

You are free to download, share and use the pdf file. You are free to print it out until I make hard copies available for sale, which will likely be sometime this spring.

You are not free to sell it in any form.

Enjoy and report back, won’t you?

I owe thanks to Terry Wyberg at the University of Minnesota, who regularly plays the “Which one doesn’t belong?” game with numbers in professional development sessions, and to my online colleagues including but limited to Justin Lanier, Megan Schmidt, Dave Peterson, Matt Enlow and Andy Rundquist.

january 2015 by robertogreco

Politicizing the Trapezoid | JD2718

may 2014 by robertogreco

"In this case, a vendor was imposing a change in definition with little warning, and no discussion. Teachers haven’t heard about it (the majority probably still haven’t), textbooks aren’t updated. And the decision was made implicitly, by accepting a test, not by people responsible to the public. AMTNYS should have worked to stop SED. Instead, they told teachers about the new definition. AMTNYS’ leaders can claim they are not an advocacy organization. But when they accept the new testing regimen without complaint, education reform, including in mathematics, without complaint, new curricula without complaint, changes made to a mathematical definition by a vendor, without complaint, and in fact transmit each of those to mathematics teachers – they are in fact adding their weight to the direction of change advocated by the Ed Reformers in Albany, they are advocating, and they are advocating against teachers and against students. I am disappointed.

Of all the bad things ed reform is doing and has done, changing a definition without discussion is not high on the list. And, in this case, its not that Coleman is out to screw kids (he is, but does he care about trapezoids? He has millions of children who he treats with disregard, what’s a silly shape to him?) It’s not that John King and Andrew Cuomo were out to get kids to get one more question wrong (they don’t care). It’s not that Barack Obama and Arne Duncan, when they pushed Common Core on the states thought about ways to change one definition. And it’s not that AMTNYS’ leadership is so badly compromised by needing to be friendly with powerless state bureaucrats that they forgot to speak up.

No, it’s just one more, small, bizarre episode: Common Core redefines Trapezoid."

commoncore
math
mathematics
geometry
2014
policy
process
trapezoids
politics
Of all the bad things ed reform is doing and has done, changing a definition without discussion is not high on the list. And, in this case, its not that Coleman is out to screw kids (he is, but does he care about trapezoids? He has millions of children who he treats with disregard, what’s a silly shape to him?) It’s not that John King and Andrew Cuomo were out to get kids to get one more question wrong (they don’t care). It’s not that Barack Obama and Arne Duncan, when they pushed Common Core on the states thought about ways to change one definition. And it’s not that AMTNYS’ leadership is so badly compromised by needing to be friendly with powerless state bureaucrats that they forgot to speak up.

No, it’s just one more, small, bizarre episode: Common Core redefines Trapezoid."

may 2014 by robertogreco

The Handheld Mathematics of Geometer Ron Resch

december 2013 by robertogreco

"Visionary applied geometer Ron Resch, who passed away in 2012, is the subject of the incredible documentary embedded above, that, while by no means new (it was produced back in the grainy days of 1970) seemed worth posting here. Over the course of its more than 40 minutes of mind-altering geometry and material experimentation, we watch Resch unfold, stretch, expand, and play with a mind-boggling wizardry of handmade models that seem to be blink in and out of the ordinary world.

Less structures, in a sense, than experimental prototypes anticipating some of the advanced geometric models of today's most high-powered graphics packages, Resch's models were supremely functional, spatially bewildering, and totally, totally awesome.

In many ways it seems oddly short-sighted of the world that Resch's work would, in the end, be most remarkable for resembling children's toys—from folding snakes to Rubik's cubes—rather than kicking off a brave new world of weird, inter-dimensional furniture and shapeshifting buildings that Resch's work implied would be only a few years away.

A Reschian city of expanding arches and pinched, fractal canopies, where walls become structures and whole neighborhoods are just by-products of massive contraptions, would be a delirious thing to live within, and Resch himself always had his eye on the architectural implications of his work.

In the film embedded above, for example, he describes a waffled, geometrically complex surface that, when combined with sound-absorbing materials, would make an ideal acoustic wall for dampening sound and enhancing privacy. Resch himself was constantly working on new forms of self-supporting origami that might someday pass for buildings.

In any case, the whole film is worth watching—but get yourself a stack of paper before you begin, because you'll be itching to fold your own mathematical shapes and infinite surfaces in no time."

[Direct link to video: https://vimeo.com/36122966

[More: https://pinboard.in/u:robertogreco/b:7715d08f716e ]

geometry
origami
ronresch
folds
folding
paper
structure
2013
geoffmanaugh
math
mathematics
design
architecture
triangles
Less structures, in a sense, than experimental prototypes anticipating some of the advanced geometric models of today's most high-powered graphics packages, Resch's models were supremely functional, spatially bewildering, and totally, totally awesome.

In many ways it seems oddly short-sighted of the world that Resch's work would, in the end, be most remarkable for resembling children's toys—from folding snakes to Rubik's cubes—rather than kicking off a brave new world of weird, inter-dimensional furniture and shapeshifting buildings that Resch's work implied would be only a few years away.

A Reschian city of expanding arches and pinched, fractal canopies, where walls become structures and whole neighborhoods are just by-products of massive contraptions, would be a delirious thing to live within, and Resch himself always had his eye on the architectural implications of his work.

In the film embedded above, for example, he describes a waffled, geometrically complex surface that, when combined with sound-absorbing materials, would make an ideal acoustic wall for dampening sound and enhancing privacy. Resch himself was constantly working on new forms of self-supporting origami that might someday pass for buildings.

In any case, the whole film is worth watching—but get yourself a stack of paper before you begin, because you'll be itching to fold your own mathematical shapes and infinite surfaces in no time."

[Direct link to video: https://vimeo.com/36122966

[More: https://pinboard.in/u:robertogreco/b:7715d08f716e ]

december 2013 by robertogreco

Polynesian Stick Charts

november 2012 by robertogreco

The Nonist on stickcharts:

"The Polynesians, scattered as they were over 1,000 islands across the central and southern Pacific Ocean, were master navigators who tracked their way over a huge expanses of ocean without any of the complex mechanical aids we associate with sea fairing. They didn’t have the astrolabe or the sextant, the compass or the chronometer. They did however have aids of a sort, which though seemingly humble, were in fact the repositories of an extremely complex kind of knowledge. Called Rebbelibs, Medos. and Mattangs, today we call them simply “Stick Charts.”

There are three kinds of stick charts. …"

marshallislands
micronesia
nonist
mapping
oceanography
geometry
history
maps
geography
cartography
stickcharts
"The Polynesians, scattered as they were over 1,000 islands across the central and southern Pacific Ocean, were master navigators who tracked their way over a huge expanses of ocean without any of the complex mechanical aids we associate with sea fairing. They didn’t have the astrolabe or the sextant, the compass or the chronometer. They did however have aids of a sort, which though seemingly humble, were in fact the repositories of an extremely complex kind of knowledge. Called Rebbelibs, Medos. and Mattangs, today we call them simply “Stick Charts.”

There are three kinds of stick charts. …"

november 2012 by robertogreco

Buckminster Fuller - Wikipedia

june 2011 by robertogreco

"He attended Froebelian Kindergarten. Spending much of his youth on Bear Island, in Penobscot Bay off the coast of Maine, he had trouble with geometry, being unable to understand the abstraction necessary to imagine that a chalk dot on the blackboard represented a mathematical point, or that an imperfectly drawn line with an arrow on the end was meant to stretch off to infinity. He often made items from materials he brought home from the woods, and sometimes made his own tools. He experimented with designing a new apparatus for human propulsion of small boats.

Years later, he decided that this sort of experience had provided him with not only an interest in design, but also a habit of being familiar with and knowledgeable about the materials that his later projects would require. Fuller earned a machinist's certification, and knew how to use the press brake, stretch press, and other tools and equipment used in the sheet metal trade."

design
technology
art
architecture
future
buckminsterfuller
childhood
froebel
kindergarten
learning
materials
systemsthinking
biography
maine
bearisland
penobscotbay
geometry
math
mathematics
toolmaking
designthinking
friedrichfroebel
Years later, he decided that this sort of experience had provided him with not only an interest in design, but also a habit of being familiar with and knowledgeable about the materials that his later projects would require. Fuller earned a machinist's certification, and knew how to use the press brake, stretch press, and other tools and equipment used in the sheet metal trade."

june 2011 by robertogreco

jeweled platypus · text · Observational math

february 2011 by robertogreco

"I like learning geometry and topology terms that make you notice and describe patterns out in the wild:"

math
mathematics
noticing
brittagustafson
observation
photography
nature
patterns
patternrecognition
reaction-diffusion
rabbitfish
rabbitfishscales
scales
angleofrepose
piles
caustics
giovannianselmo
cantenarycurves
cantenary
caustic
geometry
february 2011 by robertogreco

Mice Problem -- from Wolfram MathWorld

february 2011 by robertogreco

"In the mice problem, also called the beetle problem, mice start at the corners of a regular -gon of unit side length, each heading towards its closest neighboring mouse in a counterclockwise direction at constant speed. The mice each trace out a logarithmic spiral, meet in the center of the polygon, and travel a distance…"

math
programming
animation
geometry
via:brita
miceproblem
mathematics
february 2011 by robertogreco

Move: Choreographing You / Amanda Levete | ArchDaily

december 2010 by robertogreco

"The exhibition design was driven by the relationships between choreography and geometry, movement and form. Inspired by the photographic motion studies of the human body of Etienne-Jules Marey and Eadweard Muybridge, we have created a collection of spatial dividers which are defined by a serial transformation of a single material: a sequence of folded oscillations of Dupont Tyvek. The resulting translucent paper-like fabric ribbons, a counterpoint to the brutality of the building, rise and fall with undulating folds which simultaneously define themselves as way finding devices, partitions, suspended ceilings, and portals. These fluid spatial and formal transformations choreograph the movement of the visitor through areas of sculpture, film, archive and performance."

choreography
architecture
sculpture
eadweardmuybridge
etienne-julesmarey
anatomy
human
body
movement
geometry
form
motion
motionstudies
fabric
glvo
bodies
december 2010 by robertogreco

Google: Exploring Computational Thinking

november 2010 by robertogreco

"Easily incorporate computational thinking into your curriculum with these classroom-ready lessons, examples, and programs. For more resources, including discussion forums and news, visit our ECT Discussion Forums."

[See also: http://googleresearch.blogspot.com/2010/10/exploring-computational-thinking.html ]

computerscience
computationalthinking
via:lukeneff
algebra
biology
calculus
compsci
geometry
python
programming
math
lessons
teaching
thinking
edtech
education
elearning
danmeyer
google
science
learning
glvo
edg
srg
[See also: http://googleresearch.blogspot.com/2010/10/exploring-computational-thinking.html ]

november 2010 by robertogreco

tine de ruysser: wearable metal origami

september 2010 by robertogreco

"belgian designer tine de ruysser focused on the creation of wearable metal origami for her PhD at the royal college of art in london. one of the products she developed for her project was this shoulder cape made from copper and polyester combined in a geometric folding pattern. the unique geometry of the cape allows it to conform to the wearer’s body, fitting like a fabric rather than a solid metal. the materials consist of small squares and triangular forms made from sheet<br />

copper, connected together in a repeating pattern using the polyester. the shape of the metal gives the material its malleability. de ruysser created a number of other objects for her project including skirts, bracelets and bags." [As a wearable, I’m not convinced, but I would love to see something like this used to build flexible enclosures.]

copper
wearable
metal
glvo
flexible
folding
geometry
wearables
copper, connected together in a repeating pattern using the polyester. the shape of the metal gives the material its malleability. de ruysser created a number of other objects for her project including skirts, bracelets and bags." [As a wearable, I’m not convinced, but I would love to see something like this used to build flexible enclosures.]

september 2010 by robertogreco

Illuminations: Dynamic Paper

september 2010 by robertogreco

"Need a pentagonal pyramid that's six inches tall? Or a number line that goes from ‑18 to 32 by 5's? Or a set of pattern blocks where all shapes have one-inch sides? You can create all those things and more with the Dynamic Paper tool. Place the images you want, then export it as a PDF activity sheet for your students or as a JPEG image for use in other applications or on the web."

dynamicpaper
graphs
generator
geometry
mathematics
math
free
interactive
worksheets
graphing
september 2010 by robertogreco

YouTube - Metamorphosis of the Cube

august 2010 by robertogreco

"The Metamorphosis of the Cube is a video envisioned and created by Erik Demaine, Martin Demaine, Anna Lubiw, Joseph O'Rourke, and Irena Pashchenko. It appears in a refereed video collection, the 8th Annual Video Review of Computational Geometry, associated with the 15th Annual ACM Symposium on Computational Geometry (SoCG'99)"

geometry
math
mathematics
cubes
transformation
folding
august 2010 by robertogreco

Happy Ending problem - Wikipedia, the free encyclopedia [via: http://mrgan.tumblr.com/post/850661958/]

july 2010 by robertogreco

"The Happy Ending problem (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement:

math
mathematics
polygons
paulerdos
geometry
july 2010 by robertogreco

bruketa & zinic: kvarner visual identity

july 2010 by robertogreco

"the new visual identity for kvarner county tourism office has been developed by advertising agency bruketa & zinic. throughout history, kvarner located in croatia has been known as an intersection of four transport routes. according to bruketa & zinic, the very name kvarner evokes this quadrant, navigational spatial orientation. this is why the source of this visual identity proposal begins with the familiar symbol of the wind rose, which also includes references to navigation, four-sided spatial orientation and wind direction. this motif is then divided into simple geometrical visual elements, their simple forms and colors creating a kind of 'toolbox' for further development of the visual identity of the kvarner region and each one of its individual parts."

relationships
evolvinglogos
design
identity
graphics
logos
branding
croatia
spatial
navigation
geometry
visual
july 2010 by robertogreco

carsten nicolai: 'anti reflex'

may 2010 by robertogreco

"'anti' is a regular geometric form which represents systematic thinking and the interrelationship between mathematics, optics, art and philosophy. in appearance, it is a distorted cube, truncated at the top and bottom to obtain rhombic and triangular faces. the object reacts to the magnetic fields of bodies, enabling interaction with the visitor, while all of its mechanisms are hidden within. derived from artist albrecht dürers engraving 'melancholia i' (1514), 'anti's' black, light-absorbent surface and monolith-like crystalline shape confronts the viewer, trying both to mask its form and to disguise its function, thereby absorbing information."

art
sculpture
science
philosophy
interactive
matter
function
albrechtdürer
geometry
math
mathematics
optics
may 2010 by robertogreco

Take It to the Limit - Opinionator Blog - NYTimes.com

april 2010 by robertogreco

"What’s so charming about this calculation is the way infinity comes to the rescue. At every finite stage, the scalloped shape looks weird and unpromising. But when you take it to the limit — when you finally “get to the wall” — it becomes simple and beautiful, and everything becomes clear. That’s how calculus works at its best."

math
infinity
archimedes
pi
circles
circumference
area
calculus
mathematics
via:migurski
proof
visualization
geometry
limits
education
history
april 2010 by robertogreco

YouTube - Nature by Numbers

march 2010 by robertogreco

"A movie inspired on numbers, geometry and nature, by Cristóbal Vila. Go to www.etereaestudios.com for more info: theory behind, stills, screenshots, tutorials..."

math
mathematics
video
science
geometry
fractals
patterns
fibonacci
numbers
nature
march 2010 by robertogreco

Khan Academy

september 2009 by robertogreco

"The Khan Academy is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere.

We have 900+ videos on YouTube covering everything from basic arithmetic and algebra to differential equations, physics, chemistry, biology and finance which have been recorded by Salman Khan.

He has also developed a free, adaptive math program available here. ( Keep in mind that the web application is not fully supported and may not work properly with certain browser and/or network configurations)

To keep abreast of new videos as we add them, subscribe to the Khan Academy channel on YouTube.

The entire video library is shown below. Just click on a category or video title to start learning from the Khan Academy!"

[YouTube channel here: http://www.youtube.com/user/khanacademy ]

[via: http://smartpei.typepad.com/robert_patersons_weblog/2009/09/khan-academy---your-next-high-school---free-on-your-terms.html ]

education
learning
free
homeschool
economics
teaching
science
math
algebra
mathematics
geometry
trigonometry
physics
tutorials
youtube
calculus
online
finance
lectures
khanacademy
tcsnmy
arithmetic
We have 900+ videos on YouTube covering everything from basic arithmetic and algebra to differential equations, physics, chemistry, biology and finance which have been recorded by Salman Khan.

He has also developed a free, adaptive math program available here. ( Keep in mind that the web application is not fully supported and may not work properly with certain browser and/or network configurations)

To keep abreast of new videos as we add them, subscribe to the Khan Academy channel on YouTube.

The entire video library is shown below. Just click on a category or video title to start learning from the Khan Academy!"

[YouTube channel here: http://www.youtube.com/user/khanacademy ]

[via: http://smartpei.typepad.com/robert_patersons_weblog/2009/09/khan-academy---your-next-high-school---free-on-your-terms.html ]

september 2009 by robertogreco

sevensixfive: How to: Draw the Voronoi Diagram

september 2009 by robertogreco

"Drawing Voronoi diagrams by hand has renewed my interest in the stuff. There are lots of scripts out there for making instant vector crystal foam in just about any modeling or CAD platform, but it's more interesting for me right now to slow it down, take it step by step, and really try to understand the geometries involved. More a heuristic than an algorithm, executing it demands and reinforces the kind of zoned out close attention that almost becomes the whole point of drawing in the first place. The artifact that you get at the end it is just an unexpected bonus: the physical record left by the process of thinking out loud on paper. Below is a rough pseudocode (thanks, mike!) for building it up from a set of points."

continuouspartialattention
process
drawing
craft
voronoi
topology
visualisation
sevensixfive
geometry
structure
space
design
networks
growth
diagrams
fredscharmen
september 2009 by robertogreco

sevensixfive: Invasive Species

september 2008 by robertogreco

"This project takes the detritus from the constant construction and destruction of Baltimore's built environment into the park to form new patterns and structures embedded in the ground like reverse archaeology"

art
architecture
installation
urban
geometry
decay
baltimore
landscape
ecotopia
environment
visualization
cities
urbanism
urbandecay
glvo
invasivespecies
fredscharmen
september 2008 by robertogreco

dy/dan » Geometry: The Supplement

september 2008 by robertogreco

"This supplement comprises 2,144 slides and 1.94 GB — a lot of a/v content, in other words, some of which I did not author and do not have explicit permission to republish. Sorry about that. Every respect has been paid to Fair Use. Every effort has been made at attribution.

Textbook assignments and certain diagrams, for example, reference Discovering Geometry, a very good Geometry text. The opener miscellany, for another example, is lifted from both Snapple® caps and Vital Statistics, a reference text which is just as good as Snapple® but in a different way. If you are a copyright holder (or know one) and I missed your attribution, please let me know via dan at mrmeyer dot com and we will make that right.

The rest is yours to use under a Creative Commons attribution-noncommercial-sharealike license. This supplement is provided as is. Your suggestions are welcome and appreciated but, due to time constraints, this is not a wiki."

geometry
education
curriculum
math
powerpoint
lessons
lectures
danmeyer
howto
Textbook assignments and certain diagrams, for example, reference Discovering Geometry, a very good Geometry text. The opener miscellany, for another example, is lifted from both Snapple® caps and Vital Statistics, a reference text which is just as good as Snapple® but in a different way. If you are a copyright holder (or know one) and I missed your attribution, please let me know via dan at mrmeyer dot com and we will make that right.

The rest is yours to use under a Creative Commons attribution-noncommercial-sharealike license. This supplement is provided as is. Your suggestions are welcome and appreciated but, due to time constraints, this is not a wiki."

september 2008 by robertogreco

GeoGebra

august 2008 by robertogreco

"GeoGebra is a free and multi-platform dynamic mathematics software for schools that joins geometry, algebra and calculus. It received several international awards including the European and German educational software awards."

tcsnmy
math
geometry
algebra
calculus
education
learning
technology
opensource
visualization
freeware
august 2008 by robertogreco

Seed: The Shape of Music - How do harmony and melody combine to make music?

july 2008 by robertogreco

"Pythagoras was correct more than two and a half millennia ago: Music provides one of the clearest examples of a much deeper relation between mathematics and human experience."

consilience
geometry
math
physics
science
music
space
structure
topology
visualization
july 2008 by robertogreco

the geometry of music (26 May, 2008, Interconnected)

may 2008 by robertogreco

"Causists, dirty causists, filthy causists, are unable to see that the world is almost entirely exceptional."

music
math
geometry
future
causists
mattwebb
2008
may 2008 by robertogreco

Seed: Paola Antonelli + Benoit Mandelbrot: The curator and the mathematician discuss fractals, architecture, and the death of Euclid.

march 2008 by robertogreco

"Euclid...masterpieces of human mind...not meant to be used as textbook by millions ...meant for very small community of mathematicians...to force beginners into mathematics in this particular style was decision taken by teachers & forced upon society"

architecture
art
chaos
benoitmandelbrot
paolaantonelli
complexity
geometry
fractals
math
science
design
generalists
nonlinear
nature
euclid
teaching
learning
education
gamechanging
non-linear
alinear
linearity
march 2008 by robertogreco

glee. by Kokoromi

january 2008 by robertogreco

"Glee. by Kokoromi is a one-player collection game that uses live musical input (from your line-in or MP3 player) to create the gameplay."

audio
games
processing
sound
music
input
gaming
play
geometry
windows
mac
os
x
Linux
january 2008 by robertogreco

Theoretical physics | Geometry is all | Economist.com

november 2007 by robertogreco

"That a theory of everything might emerge from geometry would be neat, but it is a long shot. Nevertheless, that is what Garrett Lisi is proposing. The geometry he has been studying is that of a structure known to mathematicians as E8, which was first rec

science
physics
math
geometry
november 2007 by robertogreco

Collective Perception

november 2007 by robertogreco

"excerpt of SpaceCollective.org, a soon to be released, invite only information exchange dedicated to the future of everything. SpaceCollective is about to go into public beta and is issuing a limited amount of exclusive beta generation invites now."

art
blogs
collective
consciousness
culture
design
fractals
future
geometry
gotham
history
images
knowledge
life
perception
philosophy
psychology
quotes
science
space
scifi
technology
thought
evolution
futurism
november 2007 by robertogreco

Outside In

november 2007 by robertogreco

"This is a sphere turning inside out."

math
visualization
geometry
topology
video
november 2007 by robertogreco

Voronoi diagram - Wikipedia, the free encyclopedia

october 2007 by robertogreco

"a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points."

voronoi
math
mapping
geometry
algorithms
visualization
words
october 2007 by robertogreco

YouTube - Moebius Transformations Revealed

september 2007 by robertogreco

"A short film depicting the beauty of Moebius Transformations in mathematics. The movie shows how moving to a higher dimension can make the transformations easier to understand."

math
video
geometry
visualization
transformation
science
graphs
graphics
animation
september 2007 by robertogreco

PingMag - Transformable Architecture [Chuck Hoberman]

july 2007 by robertogreco

On the way to his current exhibit at the Kitakyushu Innovation Gallery, the inventor made a quick stop in Tokyo for an impressive presentation at, you guessed it, Pecha Kucha. PingMag wanted to know all about transformable architecture!

design
architecture
engineering
toys
transformation
geometry
kinetic
origami
sculpture
chuckhoberman
pingmag
july 2007 by robertogreco

Dimension-Bending Games Stretch Fabric of Space and Time

july 2007 by robertogreco

"Games are a superb environment for experimenting with new perceptual takes on geometry and physics. Designers craft these worlds from scratch, after all; they don't have to obey normal laws of reality."

education
environment
games
geometry
math
nintendo
perception
physics
reality
space
time
visualization
wii
learning
videogames
july 2007 by robertogreco

BBC NEWS | World | Middle East | Advanced geometry of Islamic art

february 2007 by robertogreco

"A study of medieval Islamic art has shown some of its geometric patterns use principles established centuries later by modern mathematicians."

math
art
history
geometry
february 2007 by robertogreco

Crease Patterns

december 2006 by robertogreco

"The origami crease pattern has an ancient history, going back to the very beginnings of origami itself. Before there were step-by-step diagrams, there were crease patterns, which served, variously, as a guide to the folder, and as decorative item form in itself. Even today, the fold-dyed paper known as itajime-washi reveals its initial crease pattern whether folded, flat, or however used. Today, however, they provide a glimpse into the mind of the origami creator, whether you are an origami artist seeking to replicate (or approximate, or build upon, or go beyond) another's work, or simply an aficionado of pattern, form, symmetry, and/or beauty. The sections linked from this page provide an entree into the world of origami crease patterns, whatever your interest or motivation.

• Crease Patterns as Art — Since the beginning of the technical revolution in the world of origami in the 1960s, the rapidly growing complexity of origami crease patterns has made them interesting and beautiful as standalone artworks. This page shows some of my own explorations into artistic crease patterns since the turn of the new millenium.

• Crease Patterns for Folders — To a small, but growing, number of origami artists, crease patterns can serve as something more than a hint, less than a guide, for how to fold a figure. If you're interested in getting into crease patterns, this page contains some thoughts and useful links.

• Crease Pattern Gallery — Forget the discussion, just show me the crease patterns! This page contains a gallery of all crease patterns on the site, along with the folded works that they correspond to."

animals
art
paper
origami
howto
design
crafts
culture
geometry
sculpture
visualization
robertlang
folding
• Crease Patterns as Art — Since the beginning of the technical revolution in the world of origami in the 1960s, the rapidly growing complexity of origami crease patterns has made them interesting and beautiful as standalone artworks. This page shows some of my own explorations into artistic crease patterns since the turn of the new millenium.

• Crease Patterns for Folders — To a small, but growing, number of origami artists, crease patterns can serve as something more than a hint, less than a guide, for how to fold a figure. If you're interested in getting into crease patterns, this page contains some thoughts and useful links.

• Crease Pattern Gallery — Forget the discussion, just show me the crease patterns! This page contains a gallery of all crease patterns on the site, along with the folded works that they correspond to."

december 2006 by robertogreco

Imagining the Tenth Dimension - A Book by Rob Bryanton

september 2006 by robertogreco

animation illustrating and explaining 0 to 10 dimensions with audio narration

animation
astronomy
geometry
math
virtual
visual
video
tutorials
time
theory
perspective
visualization
books
infographics
information
imagination
ideas
education
learning
september 2006 by robertogreco

- The Institute For Figuring -

december 2005 by robertogreco

"The Institute For Figuring is an organization dedicated to the poetic and aesthetic dimensions of science, mathematics and engineering.

The Institute’s interests are twofold: the manifestation of figures in the world around us and the figurative technologies that humans have developed through the ages. From the physics of snowflakes and the hyperbolic geometry of sea slugs, to the mathematics of paper folding, the tiling patterns of Islamic mosaics and graphical models of the human mind, the Institute takes as its purview a complex ecology of figuring."

art
culture
design
images
museums
research
science
math
visual
geometry
nature
technology
losangeles
local
workshops
visualization
textiles
drawing
complexity
graphics
galleries
The Institute’s interests are twofold: the manifestation of figures in the world around us and the figurative technologies that humans have developed through the ages. From the physics of snowflakes and the hyperbolic geometry of sea slugs, to the mathematics of paper folding, the tiling patterns of Islamic mosaics and graphical models of the human mind, the Institute takes as its purview a complex ecology of figuring."

december 2005 by robertogreco

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