Pi is wrong [!]

This site argues that that 2 * pi (= tau) would be a more rational (ha ha!) constant to use than pi. Radical proposition, dude.

Touch trigonometry

 Image by dullhunk via Flickr












I like this interactive visualization of trigonometry.

Project Euler

Image via Wikipedia

"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems."

(Leonard Euler, pictured at left, was a Swiss 18th Century mathematician.)

Useless math fact

"These and other remarkable formulas are the basis of modern computations of : you might ask how does one find such formulas? I have no idea".
                          From: http://rjlipton.wordpress.com

Proof that 2 = 1

a=b
a²-b²=ab-b²
(a+b)(a-b)=b(a-b)
a+b=b
2b=b
2=1

Can you see the problem?

Mathematics from father to son

Algebraic surfaces

I like this list of mathematical formulas for describing shapes (or, in fancy terms, 'algebraic surfaces'). You can try these out with the 'Grapher' program that Apple ships with its system (or any other 3D graphing program).

Visual Math proofs

1 + 3 + 5 + ... + (2n − 1) = n * n

I have always loved visual math proofs like these. The one above proves that the sum of 2n - 1 for any integers ranging from 1 to n is n squared. I think it is very important to understand that problems that seem hard under one representation may seem very easy if they are represented another way: sometimes we can solve problems just by changing the way we look at them.

Nicolo Tartaglia

Nicolo Tartaglia was the first to find the general method for all types of cubic equations, which include an unknown that is cubed. Tartaglia did not understand, however, that the full solution to these equations requires one to take the square root of a negative number.
Thanks to David Reid for suggesting this link.

Amazing Fibonacci sequence fact

"Each term in the Fibonacci sequence is derived by adding the two preceding terms:

0, 1, 1, 2, 3, 5, 8, 13, 21 …

Remarkably, you can use successive terms to convert miles to kilometers:

8 miles ≈ 13 kilometers
13 miles ≈ 21 kilometers

This works because the two units stand in the golden ratio (to within 0.5 percent)."

Thanks to: Futility Closet. The image, from Wikipedia's article on the Fibonacci sequence, is because many natural spirals (like the sunflower shown here) follow the Fibonacci sequence.

There is a whole website devoted to the Golden Ratio (as interesting as pi!) here.

The magically appearing square unit

Interesting puzzle: both figures above are made of identical components, yet they seem to have different areas. How could that be? Click the image for the answer.

Pi pi pi pi

Here's something you don't see (hear) every day: A song about pi.
Image from Wikipedia

Vector intro

This is a nice simple intro to the use of vectors in physics, which we were recently discussing.

Turning a sphere inside out.

This is cooler than it might seem at first.

[It is probably more detail than you want, at 21 minutes, but there is a much more complete explanation of what is actually going on here in this video.]

Polygons

Math is fun! Polygons are part of it. Ever wonder what a 100 sided polygon? Find out here and more here (bottom of page). Photo here.

Mental math tricks!

How to amaze your friends and surprise your teacher: Use these mental math tricks!