Explain the pythagorean theorem and its implications to

>>8788274
It relates the square of the length of a right angled triangles' hypotenuse to the sum of the squares of the other two sides.

>implications
https://www.fourmilab.ch/etexts/einstein/specrel/www/

>>8788274
>he wants a week worth of lectures in a 4chan post

The theorem itself is self-explanatory if you've had algebra 1. The implications are that you can derive the side length or angle of any triangle, given any combination of 3 sides or angles (except 3 angles) by clever manipulation of the formula, and you can use it in related rates problems (like finding the ground speed of a plane or the linear distance between two moving objects) using the derivative (the function that gives you the rate of change at a specific point in time)

>>8788274
its the n=2 exponent case where Fermat's Last Theorem stops being true

File: XXgsS.png (49KB, 1194x240px) Image search: [Google]

49KB, 1194x240px

This should clear things up.

>>8788955
int sum = 0;

for (int i = 1; i <= n; i++) {
sum += a[i] * v[i];
}

int side_1 = pow(double_bar(sum), 2);

Now I just need to know the code in double_bar() along with the code of the other side of the equation (which I don't fully understand the notation).

File: Pythagoras.gif (166KB, 800x600px) Image search: [Google]

166KB, 800x600px

>>8788274

>>8789279
>Now I just need to know the code in double_bar() along with the code of the other side of the equation (which I don't fully understand the notation).
Magnitude of the vector.

[math]\vec{v}=\langle v_1,v_2,...,v_n \rangle[/math]
[math]||\vec{v}||=\sqrt{v_1^2+v_2^2+...+v_n^2}[/math]

>>8789477
function double_bar(v) {
s = 0;
for (i = 0; i < v.length; i++) {
s += pow(v[0], 2);
}
return sqrt(s);
}

?

I find if you use an example when explaining the theorem it can really help, like why are there no square manhole covers?

>>8788274
I'm not sure it has many implications for a high school drop out.

>>8791105
What implications does it have to you?

>>8791198
any line or vector can be easily expressed separately with it's x- and y-components, makes thinking about certain operations and for example electromagnetic linear algebra becomes a bit more intuitive

>>8789279
>Js

Eww!

>>8788274
triangles are the hardest diamond

>>8793119
It's not even JavaScript, it's pseudo code. JS doesn't have explicit type keywords.

>>8788274

Begin with a triangle. It is made of three lines. Two of them form a perfectly right angle, and are exactly the same length. Connecting the points at the end of these lines, there is another line. What is the length of this line? You must give it a number that is indivisible. Let’s say 1, for example. For all configurations of this shape, the sum of the squared lengths of the first two sides equal that of the squared length of the third - this is true in any plane. However, you’ll find that the triangle you have just created is quite impossible. Here’s why: there is no conceivable number to describe the length of the two legs of this triangle. You must - you are required to - think beyond the dimension of the plane in which this triangle exists in order to maintain logical consistency with everything else in existence. If the third side is 1, then the area of a square made from that side would be one. So what two equal numbers could be squared and added together to make 1? They do not exist. They are in another dimension. They would have to be the square root of one-half, which would be one divided by the square root of 2, and there is no square root of two that can be rationally expressed. It is literally indescribable outside of itself.

The Pythagorean Theorem allows you to imagine impossible things.