Math Lore

The stories behind the videos

The written story behind every Math Lore video. The stories behind the numbers. The people, the dates, the sources.

3 min readThe Mutilated Chessboard Problem: Why 31 Dominoes Can't Cover 62 SquaresThe area matches exactly. The colors do not. A puzzle from a 1946 logic textbook shows how the right way of looking beats any amount of trial and error.6 min readWhy Is e = 2.718…? How Compound Interest Found the Number of GrowthNobody chose the number 2.718281828…; let growth feed on itself and it answers, in banks, in atoms, in luck and in a circle.3 min readHow Many Ways Can 4 Letters All Go in the Wrong Envelopes? The Story of DerangementsMost people guess the chance is below one third. Count the shuffles and every letter goes wrong more often than that, with e hiding in the answer.3 min readCompound Interest and the Number e: Why Your Balance Stops Near 2.718Split one year's interest into ever smaller payments and the money does not explode. It creeps up toward a single number, and Jacob Bernoulli found it first.6 min readWhat Is Pi, Really? Why π Is the Unit of Turning, Not Just 3.14Circumference over diameter is where π starts, not what it is. Follow it from Archimedes' polygons to half a turn, and to a sphere where the ratio fails.3 min readWhy the Square Root of 2 Broke the Pythagoreans: The Diagonal That Ended a ReligionA square with sides of 1 has a diagonal that no ratio of whole numbers can measure. That fact cut straight through a brotherhood that believed all is number.3 min readWhy Doubling Beats Everything: Exponential Growth, Folded Paper and a ChessboardA sheet one tenth of a millimeter thick, doubled 42 times, ends up farther away than the Moon. Here is why doubling leaves steady adding behind.7 min readWhy Is the Square Root of 2 Irrational? The Number That Broke MathematicsA square's diagonal cannot be measured by any fraction. Here is the short proof, the legend it grew, and the question it left open until 1872.