PythagoreanTheorem.net is a free, independent reference devoted to a single result: a2 + b2 = c2. Most explanations of the Pythagorean theorem stop after one diagram and two examples. This site goes further, because the theorem connects to almost everything in school mathematics — square roots, coordinates, trigonometry, vectors, proof itself — and students deserve to see those connections clearly.
What you'll find here
- A structured course, from recognising the hypotenuse to the theorem in three and more dimensions.
- Calculators that show their working step by step and give exact answers in simplest radical form, not just a rounded decimal.
- Animated proofs that move the pieces so you can see why each argument works.
- Practice material — worked examples, word problems, quizzes and printable worksheets with full answer keys.
- Pythagorean triples, real-life uses and a careful history that separates evidence from legend.
- Resources for teachers and parents, including a lesson plan and classroom activities.
How pages are written and checked
Every page answers one question completely and links to the page that owns each neighbouring topic, so you are never reading the same explanation twice. Three rules apply everywhere:
- Every number is computed, not typed. Worked examples, tables, answer keys and diagram labels are checked by machine. The tables of Pythagorean triples are generated by a program, not copied from elsewhere.
- Every diagram is drawn to scale. Coordinates are calculated, so a 3-4-5 triangle really has sides in the ratio 3 : 4 : 5, and the pieces of a dissection proof really fit.
- History is sourced and hedged. Much of what is repeated about Pythagoras is legend. Our history pages say what the evidence supports, flag what is uncertain, and point to scholarly sources such as the MacTutor History of Mathematics archive.
The site uses consistent conventions throughout: the legs are a and b, the hypotenuse is c, and in diagrams leg a is blue, leg b is orange and the hypotenuse c is green — a colour-blind-safe palette.
Who edits the site
Every page is written, checked and maintained by the PythagoreanTheorem.net team, the site's editorial staff. Pages show the date of their last revision, and the team reviews them whenever an error is reported or a source changes. You can reach the team at [email protected].
Built to be fast and accessible
Pages are plain HTML with one small stylesheet, no web fonts and no ads, so they load almost instantly even on a slow phone connection. Mathematics is rendered as text rather than images, so it stays sharp, scales with your font size and can be read by screen readers. Diagrams are lightweight inline graphics that adapt to dark mode; animations start only when you scroll to them, can be paused or replayed, and stay still if your device is set to reduce motion. Calculators run entirely in your browser. The site uses Google Analytics to count visits and see which pages are useful; the privacy policy explains what that involves.
Corrections
Mathematics leaves no room for "nearly right". If you find an error — a wrong number, an unclear step, a broken link or a historical claim you can show is mistaken — email [email protected] with the page address and what you found. Confirmed errors are corrected, and the page's "Updated" date changes to show it.
Contact
Questions, corrections, suggestions for new pages and permission requests for classroom use all go to the same address: [email protected]. Teachers are welcome to print the worksheets and cheat sheet for their own classes without asking.