February 19 Discussion

We have actually talked about the Pythagorean Triple for a little bit, and I found it really interesting. Here are two links about the Pythagorean Triple, one of which is from Wikipedia, and the other is from Wolfram Math World. I think the Math World one is probably a bit too much for our discussion, but I like its idea of showing the Pythagorean Triple in graphs.

Here is a link about the Babylonian Pythagoras (Pythagoras's Theorem in Babylonian mathematics)

Lin

Oddly enough, the smallest Pythagorean Triple (3,4,5) when cubed and summed add up to 216, which is a perfect cube, giving the equation 3^3+4^3+5^3=6^3. This has been called Plato's Number http://en.wikipedia.org/wiki/Plato's_number
Powell

• Please edit your entry to use \$\TeX\$ for the mathematics. Ethan.

For the Pythagorean Triples:
Let x, y, z be three real numbers.
If x is an odd number starting from 3, then the sum of y and z is the square of x with a difference of 1.
(If x is 1, then either one of y or z has to be 1 and the other one has to be the square root of 2, which is not a real number.)
If x is an even number starting from 4, then the sum of y and z is half of the square of x with a difference of 2.
(If x is 2, then either one of y or z has to be 2 and the other one has to be 2 times the square root of 2, which is not a real number)
Also, if x, y, z is a Pythagorean Triple, and a, b, c is another Pythagorean Triple, and a is equal to the double of x, then b is also equal to the double of y and c is equal to the double of z.

I came up with this during class, that is why I posted this as soon as the class ended on Tuesday.

Lin

• Nice! Ethan

As i was searching the internet for some good ways to learn the Pythagorean triple formula i stumbled upon a silly video using the triples. It seems silly but when you use food in examples. I'm hooked.