Section

Number theory

Figurate numbers, divisibility and primes, seen as arrangements of points rather than strings of digits.

1. 01The distribution of primes – a question of perspectiveWhy the tetractys should have anything to do with the primes, why professional mathematicians think little of the idea, and why it is still worth insisting on.
2. 02Tetractys part 1 – the order of the primesAll primes from 5 on lie in the rhythm of six, 6n ± 1. The numbers divisible by three form the axes of symmetry between them.
3. 03Tetractys part 2 – the "disorder" of the primesFrom 25 on, the multiples of 5, 7, 9, 11 … occupy the twin positions. Their grids start 10 apart and grow in steps of 4 – 10 : 4 = 2.5, like the pentagram.
4. 04The sieve of Eratosthenes and the tetractysA new look at the oldest method for finding primes. The numbers that drop out of the twin positions between 25 and 169 arrange themselves in grids 10 apart.
5. 05Simplexes and primes in the division tableThe figures of the simplexes can be fanned out into a table of all fractions. The four start figures form a grid in it, and the coprime cells have the density 6/π².
6. 06Simplexes, number theory and πThe hexagon and the three before the decimal point, squares folded into an n-gon, and figures whose angles add up to exactly one full circle.
7. 07Peter Plichta's prime number crossThe numbers arranged in rings of 24. All primes from 5 on lie on just eight rays, which form a cross.
8. 08Remarkable facts about the number 241 × 2 × 3 × 4 = 24. Four rhythms of six before 25, 24 symmetries of the tetrahedron, 24 edges in the primal fractal and the kissing number of the fourth dimension.
9. 09The tetractys and the Cartesian coordinate systemThe four basic operations of arithmetic in the four quadrants of a coordinate system. To understand the primes, you have to switch back and forth between calculating and drawing.