Equations that involve trigonometric functions can have infinitely many solutions. For example, the solution to the equation tan(θ)=1 is θ = π/4 + kπ, where k is any integer. In order to obtain a unique solution to the equation, we define the "arc" functions: inverse trigonometric functions that return a

## Tag: **Math**

Last week I was chatting with some mathematicians and I mentioned the blog post that I wrote last year on the distribution of Pythagorean triples. In my previous article, I showed that there is an algorithm that uses matrix multiplication to generate every primitive Pythagorean triple by starting with the

Pascal's triangle is the name given to the triangular array of binomial coefficients. The nth row is the set of coefficients in the expansion of the binomial expression (1 + x)n. Complicated stuff, right? Well, yes and no. Pascal's triangle is known to many school children who have never heard of polynomials

When I studied high school geometry, I noticed that many homework problems involved right triangles whose side lengths were integers. The canonical example is the 3-4-5 right triangle, which has legs of length 3 and 4 and a hypotenuse of length 5. The triple (3, 4, 5) is called a

Although I currently work as a statistician, my original training was in mathematics. In many mathematical fields there is a result that is so profound that it earns the name "The Fundamental Theorem of [Topic Area]." A fundamental theorem is a deep (often surprising) result that connects two or more

Prime numbers are strange beasts. They exhibit properties of both randomness and regularity. Recently I watched an excellent nine-minute video on the Numberphile video blog that shows that if you write the natural numbers in a spiral pattern (called the Ulam spiral), then there are certain lines in the pattern

My daughter's middle school math class recently reviewed how to compute the greatest common factor (GCF) and the least common multiple (LCM) of a set of integers. (The GCF is sometimes called the greatest common divisor, or GCD.) Both algorithms require factoring integers into a product of primes. While helping

Birds migrate south in the fall. Squirrels gather nuts. Humans also have behavioral rituals in the autumn. I change the batteries in my smoke detectors, I switch my clocks back to daylight standard time, and I turn the mattress on my bed. The first two are relatively easy. There's even

Today is the birthday of Bernhard Riemann, a German mathematician who made fundamental contributions to the fields of geometry, analysis, and number theory. Riemann is definitely on my list of the greatest mathematicians of all time, and his conjecture about the distribution of prime numbers is one of the great