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← 📐 Mathematics · usually met in Std 5-12

Geometry

The mathematics of shape, size and position — and the place where most students first meet the idea of proof.

a² + b² = c² a² = 9 b² = 16 c² = 25 The square drawn on the longest side has exactly the same area as the two smaller squares put together. 3 and 4 and 5 is the smallest whole-number case, and masons have used a knotted rope of 12 units to make a true right angle for thousands of years. The relation appears in the Shulba Sutras, written in India for building altars, before Euclid. A proof is not an example: one case that works proves nothing, and one case that fails disproves everything.
Drawn for Star Student.

Euclid set out a handful of definitions and five postulates and derived hundreds of results from them, and that structure — assume as little as possible, prove the rest — became the model for mathematics itself. Pythagoras' theorem, that the square on the hypotenuse equals the sum of the squares on the other two sides, is the single most used result in the subject.

Geometry is also the oldest applied mathematics there is. The Shulba Sutras, written for the precise construction of fire altars in ancient India, contain geometric constructions and a statement of the right-triangle relation well before Euclid. Surveying, navigation, architecture and computer graphics all run on the same ideas.

Worth knowing

  • The angles of a triangle add to 180° on a flat surface — on a sphere they add to more, which is not a mistake but a different geometry.
  • A proof is not an example. One case that works proves nothing; one case that fails disproves everything.
  • Coordinate geometry, Descartes' idea of putting shapes on axes, is what joined geometry to algebra.

Want to see it moving? Search YouTube for “Geometry” ↗ — we send you to the search rather than to one video, because a link to one video eventually rots.

See also

📐 Algebra📐 Pi📐 Number systems

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Last gone through: 1 October 2026 · How these entries are written

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