robertogreco : pi   4

Pi Day is a lie: celebrate tau, the true circle constant instead - The Verge

"But Palais and Hartl’s arguments both boil down to some basic math. Step back in time to when you first learned geometry and recall the simple origins: no matter what circle you’re using, if you divide the circumference of the circle by the diameter, you’ll get the same answer: an endless number, starting with the digits 3.14159265... (aka pi).

And right there is the fundamental flaw. The thing is, we don’t actually use diameter to describe circles. We use the radius, or one-half the diameter. The circle equation uses the radius, the area of a circle uses the radius, and the fundamental definition of a circle — “the set of all points in a plane that are at a given distance from a given point, the center” — is based on the radius. Plugging that into our circle constant equation gives us a new circle constant equivalent to 2π, or 6.28318530717..., colloquially referred to with the Greek letter τ (tau). Switching to τ isn’t making some arbitrary change for the sake of it. It’s bringing one of the most important constants in math in line with how we actually do math."
math  mathematics  pi  2019  vihart  2018  tau  numbers  culture
march 2019 by robertogreco
Take It to the Limit - Opinionator Blog - NYTimes.com
"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