Archive for the ‘Beauty’ Category

Rolling regular n-gons on catenary “roads”

Sunday, July 25th, 2010

Here's an interesting exploration, illustration courtesy of Mathematica: There's a nice animated illustration at Mathematica. A particularly interesting case of a roulette is a regular n-gon rolling on a "road" composed of a sequence of truncated catenaries, as illustrated above. This motion is smooth in the sense that the geometric centroid follows ...

Granddaddy of fractals on TED

Wednesday, July 21st, 2010

From TED: At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated. Here's some biographical information on Mandelbrot: Studying complex dynamics in the 1970s, Benoit Mandelbrot ...

Nature by Numbers video

Sunday, July 11th, 2010

Here's a delightful video that shows a nice relationship of numbers, geometry, and nature. [youtube]http://www.youtube.com/watch?v=kkGeOWYOFoA[/youtube] Hat tip to Don Cohen, the Mathman. SHARETHIS.addEntry({ title: "Nature by Numbers video", url: "http://wildaboutmath.com/2010/07/11/nature-by-numbers-video/" });

Euler’s identity via triangles and spirals

Tuesday, July 6th, 2010

Brian Slesinsky has a brilliant slide presentation on a very non-traditional way to derive Euler's identity. A couple of years ago I reviewed a great book that builds the foundation necessary for the proof. Slesinsky has a very different yet very elegant approach. It ties together these concepts: Multiplication of complex ...

Plane tiling proof of …

Saturday, July 3rd, 2010

Simon and Schuster sent me a copy of Alex Bellos' new book: Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math. The book is remarkable. Alex Bellos is a gifted journalist who traveled around the world to interview people who had interesting stories to tell. The ...

Super elegant proof without words

Friday, July 2nd, 2010

David Wood commented on my beautiful proof without words post: Here is my favourite proof without words: http://www.ms.unimelb.edu.au/~woodd/photo/photo-19.jpg This first appeared in a Chinese textbook about 3000 years ago! And of course, the picture proves …. It's a remarkable proof. I have seen similar ones but not this one. It's remarkably elegant. Here's the image from ...

How the St. Louis Arch got its shape

Monday, January 18th, 2010

I found this wonderful short video on Science Friday by mathematician Robert Osserman on the Math behind the St. Louis Gateway Arch. This video is a great testament to the beauty of mathematics. Watch it and tell us if you agree. SHARETHIS.addEntry({ title: "How the St. Louis Arch got its shape", url: "http://wildaboutmath.com/2010/01/18/how-the-st-louis-arch-got-its-shape/" });

Fractal Foundation fun

Tuesday, February 12th, 2008

In my neck of the woods in northern New Mexico, the Fractal Foundation lives the mission of inspiring interest in science, Math, and Art through the beauty of fractals. The Foundation puts on fractal-related programs in schools and takes them on the road. The Foundation also sponsors a very popular ...

Flexagon fun for the whole family

Thursday, December 13th, 2007

If you've never heard of flexagons you're in for a treat. Flexagons are flat paper constructions, some of which are really easy to make, that are tremendously fun to play with because you "flex them", hence the name, to reveal more than the two sides that you would expect to ...

Phi: It’s everywhere you look

Wednesday, October 10th, 2007

Phi, also known as the golden ratio or the divine proportion, is one of the great mathematical constants. It is equal to a little more than 1.6 and is a most interesting irrational (but not transcendental) number. Phi has a fascinating connection with the Fibonacci series, it can be derived ...