<p>You aren’t being stupid, I downloaded a calculator that can graph in 3-D and just played around. That’s the coolest graph I’ve been able to make. It doesn’t have an other significance; I’m only in BC so I’m lost when it comes to 3-D.</p>
<p>Except you need the Pythagorean Theorem to prove law of cosines? Which ends up being circular logic. But maybe there’s another proof I don’t know about.</p>
<p>This equation is really cool:
**
i^i = 1/sqrt(e^pi) **</p>
<p>RacinReaver: “the integral of Exp[-z²] from negative infinity to infinity is the square root of pi”
You can just change the variable, multiply the expression by itself to get the square of the integral, integrate in polar coordinates, and take the square root.</p>
<p>Shravas: “Except you need the Pythagorean Theorem to prove law of cosines? Which ends up being circular logic. But maybe there’s another proof I don’t know about.”
No, the law of cos generalizes the Pythagorean theorem. This means that the Pythagorean theorem is merely a special case of the law of cos (i.e. the case where the angle is 90 deg). You don’t use the Pythagorean theorem to prove the law of cos; rather, you use the law of cos to prove the Pythagorean theorem. The law of cos can be derived from a set of basic relationships between the sides of a triangle. </p>
<p>PM me if anyone wants more detail lol. I love math and would be happy to explain :)</p>