Fun with the Dot Product (Math = Patterns)
Imagine this. You have a terribly strong desire to learn as much math as you can. You know that people do research in math, whatever that...
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Jonathan
Nov 15, 2021
Rectangles in Polar Coordinates
Circles in rectangular coordinates...Rectangles in polar coordinates? This is a bit of a goofy one. Why? Well, I want to figure out...
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Jonathan
Nov 15, 2021
The Integral of Csc(θ)
What is the integral of cscθ? Usually this is done by telling you to multiply by blah/blah where blah is some expression that comes...
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Jonathan
Oct 13, 2021
The Arithmetic Derivative (Part 3)
Let us count The nice thing about the arithmetic derivative is that it takes a natural number to another natural number. This leads to...
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Jonathan
Oct 12, 2021
The Arithmetic Derivative (Part 2)
Our first pattern So we've taken the usual rules for differentiation and applied them to natural numbers: D(ab) = aD(b) + D(a)b with...
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Jonathan
Oct 9, 2021
The Arithmetic Derivative (Part 1)
An introduction If you've done calculus, then you've talked about differentiation. We usually talk about this in terms of "linear...
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