Departure question
Read the world behind shapePort 1 of 13Where two intuitions collide
A beautiful equation linking integer squares also revealed lengths that no ratio of integers could express.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
The sum of the areas of the squares on the legs of a right triangle equals the area of the square on its hypotenuse. Related number lists and geometric rules survive in Mesopotamian, Indian, Chinese, and Greek traditions, so the result should not be reduced to one discoverer. Euclid's Elements contains a general proof, and the relation remains a standard tool for Euclidean distance.
In a right triangle, the square of the hypotenuse equals the sum of the other two squares. Related calculations and proofs appear in Babylonian, Indian, Chinese, and Greek sources.
Q.a=3, b=4 → c=?
Q.a=5, b=12 → c=?
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
The Babylonian clay tablet Plimpton 322 records number patterns related to Pythagorean triples such as 3–4–5 and 5–12–13, long before a surviving general proof.
The recorded place matches a canonical map anchor
Continue this scene on the mapIn the Greek mathematical tradition, the relationship was established for every right triangle rather than only for numerical examples — a high point of the Pythagorean belief that number orders the world.
The recorded place matches a canonical map anchor
Continue this scene on the mapFor a square of side 1, the diagonal is √2, which is not a ratio of integers. The result emerged within the Pythagorean tradition, while the discoverer and circumstances remain uncertain.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearWith the coordinate plane, the distance formula between (x₁,y₁) and (x₂,y₂) became the Pythagorean theorem written in algebraic language.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearGPS coordinate calculations, distance in computer graphics, Euclidean distance in machine learning, and signal norms — the theorem is evaluated thousands of times in each rendered frame.
Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.
No concept belongs to one person
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Similarity and length ratios encouraged the old intuition that space could be described by ratios of integers.
Open the number voyage
The diagonal √2 of a unit square shows that fractions cannot fill all of space.
Open the number voyage
Rational and irrational numbers must coexist to place every length on one continuous line.
Open the number voyage
Concept genealogy
Concepts arriving from before
No direct prerequisite port is curated yet.
Current port
Pythagorean Theorem
Concepts opened from here
Only direct editorial links are shown; this is not a complete learning order or historical influence line.
