Blog
Occasional Random thoughts from us.
Floating-Point Numbers: Why 0.1 + 0.2 Isn't Exactly 0.3
In almost every programming language, 0.1 + 0.2 gives 0.30000000000000004. It isn't a bug. Here is the binary math behind it, the real disasters rounding has caused, and how to handle it correctly.
Celestial Calculations: How Astronomers Use Math to Measure the Universe
Astronomy, at its heart, is a mathematical science. From calculating the distances to faraway stars to determining the sizes of celestial bodies, math…
Binary, Hexadecimal, and Why Programmers Love Base 16
Every hex digit is exactly four bits, which makes base 16 a perfect shorthand for binary. Here is how to convert between them in your head, and where hex shows up in colors, memory and network addresses.
How Computers Represent Numbers
In a computer, 127 + 1 can equal −128. Here is how integers, two's complement, overflow and floating point really work, and the famous bugs they caused.
Why Computers Use Binary
Mathematically, base 3 is the most efficient number base, and the Soviet Union built ternary computers. So why did the world settle on 0s and 1s? Physics, noise and Boolean logic.
Why Percentages Are So Easy to Get Wrong
A 50% gain followed by a 50% loss leaves you down 25%. Percentages hide their base, and that one detail causes most percentage mistakes. Here are the traps and how to avoid them.
Why Averages Can Lie: Mean, Median, Mode, and Distribution
When the U.S. Air Force measured 4,063 pilots in 1950, not one was average on all ten body dimensions. Here is why a single average hides so much, and what to use instead.
The Math Behind Lotteries: Expected Value Explained
Powerball odds are 1 in 292,201,338. Here is how that number is calculated, what a $2 ticket is really worth, and why even a record jackpot rarely makes it a good bet.
Unlocking Insights with Regression Analysis: Real-World Applications and Examples
Regression analysis is a powerful statistical method used to model the relationship between a dependent variable and one or more independent variables. It…
The Mathematics of Gambling: Why the House Usually Wins
A casino doesn't need to win most bets. It needs a small edge and a lot of bets. Here is how house edge, variance and the law of large numbers work together.
How Insurance Companies Use Mathematics to Price Risk
An insurer can't predict whether your house will burn down, but it can predict almost exactly how many of 10,000 houses will. That gap is the whole business.
G.H. Hardy: The Paragon of Pure Mathematics and His Enduring Impact on Analysis
Godfrey Harold Hardy, universally known as G.H. Hardy, remains a monumental figure in the realm of pure mathematics, particularly celebrated for his…