Blog
Occasional Random thoughts from us.
Why Negative Numbers Exist
European mathematicians called them "absurd" and "false" into the 1700s. Here is why negative numbers were resisted for centuries, and why mathematics can't work without them.
Why Division by Zero Doesn't Work
It isn't that nobody has figured out 1 ÷ 0. It's that every possible answer breaks arithmetic. Here is why, what 0 ÷ 0 means, and a warship that stopped dead from this bug.
How to Calculate Compound Interest
Compound interest earns interest on your interest. Here is the formula A = P(1 + r/n)^(nt), step-by-step examples for different compounding frequencies, regular contributions, and how Jacob Bernoulli discovered e.
How to Calculate the Distance Between Two Points
The distance formula is just the Pythagorean theorem on a grid. Here is how to use it in 2D and 3D, with worked examples, plus the "taxicab" distance and the formula GPS uses on a round Earth.
How to Convert Hexadecimal to Decimal
Hex digits run 0–9 then A–F, and each place is worth 16 times more than the one to its right. Here are two methods to convert hex to decimal, with examples from web colors, emoji code points and memory addresses.
How to Convert Radians to Degrees
Multiply radians by 180/π to get degrees. Here is the formula with worked examples, how to handle π in the answer, angles larger than a full turn, and why a circle has 360 degrees in the first place.
How to Convert Degrees to Radians
Multiply degrees by π/180 to get radians. Here is the formula, a conversion table for common angles, worked examples, and why programming languages and calculus insist on radians.
How to Convert a Decimal to a Fraction
Terminating decimals, repeating decimals and long approximations each need a different method. Here is how to turn 0.375, 0.2727… and 3.14159 into fractions, step by step, with a trick for any repeating pattern.
How to Convert Binary to Decimal
Every binary digit is a power of 2. Here are two methods to convert binary to decimal, the place-value method and a faster doubling trick, plus binary fractions and negative numbers.
How to Calculate the Volume of a Sphere
Double a ball's radius and its volume grows eightfold. Here is the sphere volume formula V = 4/3 πr³, worked examples from a basketball to Earth, and the clever principle two ancient mathematicians used to prove it.
How to Calculate a Z-Score
A z-score tells you how many standard deviations a value is from the average, which lets you compare scores from completely different tests. Here is the formula, worked examples, and how to turn a z-score into a percentile.
How to Calculate a Weighted Average
Your final grade, your GPA, stock market indexes and inflation figures all use weighted averages. Here is the formula, step-by-step examples, and the mistake that makes simple averages give the wrong answer.