I’ve already presented and proved the rule for modular addition, so for a sense of completeness, but mostly to satisfy my OCD, now I’ll cover the rule for modular subtraction. When doing subtraction in modular arithmetic, the rule is: If we subtract integer from integer and calculate the difference modulo , we get the same answer …
Category: Math
Dec 31 2015
Modular Addition Rule Proof
Addition in modular arithmetic is much simpler than it would first appear thanks to the following rule: This says that if we are adding two integers and and then calculating their sum modulo , the answer is the same as if we added modulo to modulo and then calculated that sum modulo . Note that …
Nov 18 2015
Binary Signed Integers – Signed Magnitude
We humans and our meat computers don’t have any trouble recognizing the sign of a number. If there is a minus sign, “-,” in front of a number, that number is negative. If a number is prefixed by a plus sign, “+,” or, the more likely case, has no prefix at all, then the number …
Aug 28 2015
The Law of Cosines
So we recently covered the Pythagorean Theorem, and I am betting you’ve got at least one concern. No, I don’t mean about whether or not Planet X has begun cutting a destructive swath across our solar system. I mean in regards to calculating the length of the side of a triangle if you know the other …
Aug 13 2015
Pythagorean Theorem Proof
It may very well be the second most famous equation of all time, outshone only by that braggart Einstein’s mass–energy equivalence equation. But for those of us that aren’t theoretical physicists, the Pythagorean Theorem is likely to play a fundamental role in many of the calculations we do whether we realize it or not. Everyone knows …
Nov 15 2014
Euler’s Formula
Besides being an obvious lady killer, Swiss mathematician Leonhard Euler gifted the world with some pretty important mathematical concepts, notational conventions, and formulas. I almost feel bad about the fact that I couldn’t even spell his name correctly until I was well into adulthood. You are probably thinking, “Sure, he had a bitchin’ robe, and for …
Nov 10 2014
Complex Numbers and their Geometry
(Note: I lied. This will be my first “neural dump.” I began writing about Euler’s Formula, but felt what follows was worthy of its own post and a better foundation for what will follow when I tackle Euler.) Complex numbers arose from the fact that there is no solution for in the equation in , …