Geometry

Key people

• ArchimedesGreek mathematician and physicist (c. 287 – c. 212 BC)
• PythagorasGreek philosopher and mathematician (c. 570 – c. 495 BC)
• EuclidAncient Greek mathematician (fl. 300 BC)
• David HilbertGerman mathematician (1862–1943)

Timeline

• 1890 BC1890 BC), and the Babylonian clay tablets, such as Plimpton 322 (1900 BC).
• 1800 BCThe earliest known texts on geometry are the Egyptian Rhind Papyrus (2000–1800 BC) and Moscow Papyrus (c.
• 19001900, with a theorem called Hilbert's Nullstellensatz that establishes a strong correspondence between algebraic sets and ideals of polynomial rings.
• 2005According to (Hayashi 2005, p.

Read

• Non-Euclidean geometryH. S. M. Coxeter · 1942Book
• Calculus with analytic geometryHoward Anton · 1980Book
• The calculus, with analytic geometryLouis Leithold · 1967Book
• GeometryLee Stiff · 1995Book

Watch

• Most People Miss This Hidden Geometry LogicLogic BoosterVideo
• Can you solve for X and Y? | (Rectangle) | #math #maths | #geometryPreMathVideo
• Basic geometry: language and labels | Introduction to Euclidean geometry | Geometry | Khan AcademyKhan AcademyVideo

Listen

• Trigonometry & Geometry PapapodcastsPapaPodcastsPodcast
• Deep Dive into Topics from Advanced GeometrySam VanHeestPodcast
• The Geometry LessonCheris SouthPodcast
• Geometry 101Lauren ThomasPodcast

Voices to follow

• Igor Rivin@regiusmath · XRussian-Canadian mathematician
• Richard BorcherdsYouTubeMathematician
• Noah Giansiracusa@ProfNoahGian · XPh.D. Brown University 2011
• Henry SegermanYouTubeAmerican mathematician (born 1979)

Debates

• Is Euclidean geometry still the most relevant form of geometry?One view: Yes, Euclidean geometry remains foundational for many practical applications like architecture and engineering due to its intuitive rules for flat spaces. · Another: No, non-Euclidean geometries are crucial for understanding curved spaces, such as in cosmology (general relativity) and advanced computer graphics.Open question
• Is geometry primarily a visual or an abstract subject?One view: Geometry is fundamentally visual, relying on diagrams and spatial intuition to understand shapes, positions, and properties. · Another: Geometry is primarily abstract, built upon axioms and logical proofs that transcend visual representation, leading to complex theories.Open question

Glossary

• PointA location in space with no size or dimension.
• LineA straight, one-dimensional figure with no thickness, extending infinitely in both directions.
• PlaneA flat, two-dimensional surface that extends infinitely in all directions.
• AngleThe space formed by two rays or line segments sharing a common endpoint.
• PolygonA closed two-dimensional shape made up of straight line segments.
• TheoremA statement that has been proven true based on previously established statements.

Careers

Roles this can lead toward

Threads 9

Where this connects to other fields — and why it's worth knowing.

• Elections & Voting Politics

  Imagine drawing voting-district lines so twisty they look like a splattered inkblot, all to cram your rivals' voters into one district and scatter the rest. That's gerrymandering, and courts now catch it with actual geometry: they measure how weird and contorted a shape is. If a district looks like a crab that got run over, the math flags it as rigged.

• Philosophy of Science Philosophy

  For 2,000 years people were sure geometry gave us certain, obvious truths about space, like 'parallel lines never meet.' Then mathematicians built perfectly good geometries where they do meet, on curved surfaces. Turns out our universe really is curved, so the 'obvious' truths were just guesses about our flat little corner, not certainties baked into the mind.

• Cartography and Map Design Geography

  Try to flatten an orange peel and it always tears or crumples; you simply can't make a sphere lie flat without stretching it. That's why every flat map of Earth lies a little, blowing up Greenland or bending shapes. Mapmakers aren't clumsy; they're up against a proven math theorem (Gauss's) that says perfect flattening is flat-out impossible.

• Art History & Movements Arts

  Renaissance painters figured out how to make flat paintings look deep by drawing railroad-track lines that meet at a single 'vanishing point' on the horizon. That point is where parallel lines meet at infinity, a genuinely deep math idea. The painters discovered it with brushes decades before mathematicians wrote down the geometry of it.

• Growth, Scaling, and Going Global Business

  You can't just blow a mouse up to elephant size, because its bones would snap. When something doubles in size, its volume grows way faster than its surface, so its guts, cooling, and support all need redesigning. A company hits the same wall: a startup can't just get bigger, it has to rebuild its plumbing of managers and systems.

• Borders and Geopolitics Geography

  A treaty says the border runs along a coastline for a fixed number of miles. But zoom in and coastlines wiggle around every rock and inlet, so the more finely you measure, the longer it gets, with no final number. That's the coastline paradox, which means 'the border is exactly X miles long' is quietly a fiction.

• Countries, Capitals & Continents Geography

  No flat map of Earth can ever be fully accurate. A mathematician named Gauss proved you can't flatten a ball without stretching sizes or angles somewhere. So every world map you memorized is lying to you, and the math says it has no choice.

• Renaissance and Enlightenment History

  Renaissance painters wanting rooms to look deep and real invented perspective, the trick where lines shrink toward a point. That trick was actually solid geometry. It later grew into real math and, centuries on, powers the graphics in your video games.

• Black Holes Science

  Gravity isn't really a force pulling you — it's space itself being bent, like a ball rolling into a dip. To describe that, Einstein grabbed a weird curved-space geometry a mathematician had dreamed up decades earlier for no practical reason at all. "Useless" math just waited to become reality.