Author: MathFish

Suppose you have a set $S$ of $N$ numbers: $$\displaystyle S = \{x_1, x_2, x_3, \cdots, x_N\}$$ How many different products can be formed by multiplying at most $F$ members of $S$, allowing repetitions? For example, take $S = \{a,b,c,d\}$. Then the distinct products are: Number of factors Products 1 $$\displaystyle a, b, c, d$$ … Read More “Counting Products When Factors Count” »

1. Introduction One might remember from high-school precalculus class something called the Law of Sines, and might even remember what it is because it has a memorable pattern: $ \displaystyle \frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c} \ \ \ \ \ (1)$ where $a$, $b$, and $c$ (lowercase) are the side lengths and $A$, $B$, and … Read More “Law of Sines for Tetrahedra” »