Don’t trust the small numbers
In mathematics, the Pólya conjecture is true for every natural number up to 906,150,256… and then it’s not.
Category: Mathematics & statistics
Abnormal normal dice
A pair of Sicherman dice have numbers ranging from 1 to 8 on their faces, but roll two of them together and they produce the same totals as a pair of normal dice.
Experimental pi
If you have a piece of striped paper and some sticks, you can estimate the value of pi through a simple experiment.
Will Rogers paradox
Someone (not Will Rogers) once joked that “When the Okies left Oklahoma and moved to California, they raised the average intelligence level in both states.” This quirk of statistics has some surprising implications for cancer survival rates.
The Yale blackboard rebellion
In 1830, nearly half of the mathematics class at Yale was expelled for refusing to use a blackboard in their exams.
Da Vinci’s fractal trees
Leonardo da Vinci observed that tree branches together are always as thick as the trunk beneath them. This is true, and there are some good ideas why.
Cosmic ladder (Part 2)
To measure distances in deep space, you need to look for candles in the darkness. [2 of 2]
Cosmic ladder (Part 1)
It’s a lot more difficult to measure distances in space than you might think. [1 of 2]
Ghost leg
Ghost leg is a technique to randomly match up two groups – assigning a list of chores to a list of people, for example. And all you need is a drawing of a ladder.
Mathematical collective
Since 1939 an author named Nicolas Bourbaki has published a series of volumes on pure mathematics. But Bourbaki does not exist.
Math homework
In 1939 a student at UC Berkeley copied down two homework problems from the class blackboard. He solved them in a few days… and then discovered that they were two of the thorniest unsolved theorems in statistics.
Mathematical coincidence
A billionth of a century is approximately pi seconds. The diameter of the Earth is roughly half a billion inches.
The birthday paradox
Put 70 people in a room and there’s a 99.9% chance that two of them share a birthday. Why?
Prehistoric mathematics
The Ishango bone, found in what is today part of the Democratic Republic of the Congo and dating back 20,000 years, may contain some of the earliest evidence of mathematical thought.
Infinity and beyond
The set of natural numbers is infinite: 1, 2, 3…. The set of real numbers is also infinite: 0.1, 0.11, 0.12, 0.2… but it’s larger than the infinity of natural numbers. Georg Cantor devised an elegant argument to prove these different infinities.
First vanishing point
Masaccio’s Holy Trinity is possibly the earliest surviving work of art to use a single vanishing point. His work and that of Brunelleschi triggered a Renaissance explosion of mathematical perspective in art.