# Category Archives: mathematics

## Make a dice-rolling simulation in C#

This example performs a simulation of rolling two six-sided dice. It’s related to my book Interview Puzzles Dissected, which includes several examples that involve rolling dice. When you enter a number of trials and click Roll, the program uses the … Continue reading

## Draw the Weierstrass function in C#

The Weierstrass function was discovered by Karl Weierstrass in 1872. It’s an odd function that is continuous everywhere but differentiable nowhere. I’ll explain what that means shortly. Here’s the function: Here: The following two sections explain what it means to … Continue reading

## Calculate Fibonacci numbers in several ways in C#

For some background on Fibonacci numbers and φ, see Examine the relationship between the Fibonacci sequence and phi in C#. This example shows several ways to calculate Fibonacci numbers. While this is mostly for curiosity’s sake, this example does demonstrate … Continue reading

## Find random prime numbers in C#

The example Probabilistically determine whether a number is prime in C# explains an algorithm for determining whether a number is prime with any desired level of certainty. After you add that method to your algorithmic toolkit, finding large prime numbers … Continue reading

## Determine whether a number is prime in C#

This is a cool little algorithm that uses some clever mathematics. This algorithm and several related algorithms are described in my book Essential Algorithms: A Practical Approach to Computer Algorithms. I think it’s a really good book (and it’s gotten … Continue reading

## Animate rainbow colors in C#

The example Map numeric values to and from colors in a color gradient in C# draws a color gradient that uses rainbow colors. This example animates that one. When you click on the color gradient, the following code starts or … Continue reading

## Animate exploding 3-dimensional pie slices in C#

The example Draw 3-dimensional pie slices in C# shows how to highlight one or more 3-D pie slices by “exploding” them. This example draws even more attention to the exploded pie slices by animating their explosion. The program controls the … Continue reading

## Calculate where a line segment and an ellipse intersect in C#

Finding the intersection between a line segment and an ellipse requires a lot of mathematics. It’s not particularly hard mathematics, but if you’d rather skip it, you can use the following links to jump to the other parts of this … Continue reading

## Produce a repeatable series of “random” numbers in C#

The Random class can generate a series of pseudo-random numbers. They’re called “pseudo-random” rather than “random” because the numbers are generated by a mathematical algorithm rather than by some completely unpredictable process such as observing a source of radioactive decay … Continue reading

## Book Review: The Manga Guide to Linear Algebra

(Occasionally I post reviews of book that I think may interest programmers, in this case admittedly only those with a mathematical inclination.) The Manga Guide to Linear Algebra   \$24.95, 264 pages, 2012 By Shin Takahashi No Starch Press ISBN … Continue reading