Articles
Guides and resources about math education.
Angles and Parallel Lines: The Hidden Rules of Geometry
A line crossing two parallel rails makes eight angles — and once you know one of them, all eight are decided. Meet corresponding, alternate interior, and same-side pairs, the carpenter's one-angle shortcut, and why the rules quietly prove that every triangle totals 180 degrees.
Surveys and Sampling: Asking the Right People
A survey's fate is sealed before the first answer is written — by who you ask, when you ask, and how you ask. Meet the mirror test, why 1,000 careful strangers beat 10,000 eager volunteers, and the three questions that catch a biased poll before it fools you.
Correlation vs Causation: Two Things That Travel Together
Two numbers rise together and our brains immediately write a story. Meet the correlation coefficient, the three-step detective test that separates a real cause from a coincidence, and the red flags that expose a hidden third factor before it fools you.
The Normal Curve: Why the Bell Is Everywhere
Heights, test results, measurement errors, and a hundred other things all pile into the same bell shape. Meet the normal curve, the 68-95-99.7 rule that makes it useful, and the one warning that keeps it honest: not everything is a bell.
Standard Deviation and Variance: Measuring the Spread
The average tells you where the data is centered; the spread tells you how wide it wobbles. Meet the recipe behind variance and standard deviation — why we square the distances, what n minus 1 is doing, and how one number becomes a ruler for spotting unusual results.
Expected Value: The Number That Predicts Luck
Expected value is how you price luck: weight every outcome by its chance, add the results, and you get a forecast no gut feeling can match. Learn the formula, why it is not the same as an average, and how casinos, insurance, and everyday “should I?” decisions quietly lean on it.