Wikipedia

User:XOR'easter/Circular reasoning

< User:XOR'easter

This is a workspace for material related to improving the article Circle, which is currently under-cited, heavy on bullet points, disorganized, etc.

Basic terminology

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Metrical properties

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Circumference, area, etc.

Characterizations and representations

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Locus of points equidistant from a common center

Curve of constant curvature

Apollonian circles

Description in various coordinate systems

Euclidean plane geometry

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Central and inscribed angles

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Circles in triangle geometry

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Cyclic quadrilaterals and polygons

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Ptolemy's theorem

Cyclic polygon

Intersecting chords and secants

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Pencils of circles

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Intrinsic geometry of the circle

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Circular motion and trigonometry

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Circles in solid geometry

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Non-Euclidean and inversive geometry

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Representation using complex numbers

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Oriented circles

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Circles as conic sections

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Topological circles

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Generalizations

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Spheres of arbitrary dimension.

Curves of constant width?

Lp space

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Inscribed

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Circumscribed

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Curves found by transformation

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Pedal, caustic, etc.


Applications

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Geometry bookshelf

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  • Abramson, Jay; et al. (2024). Algebra and Geometry 2e (digital ed.). OpenStax. ISBN 978-1-951693-40-4. Free textbook at the high-school level.
  • Byrne, Oliver (2013) [1847]. The First Six Books of the Elements of Euclid (facsimile ed.). TASCHEN GmbH. ISBN 978-3-8365-4471-9.
  • Cheng, Eugenia (2023). Is Math Real? How Simple Questions Lead Us To Mathematics' Deepest Truths. Basic Books. ISBN 978-1-541-6-01826. Some relevant material on how to think about sines and cosines.
  • Coolidge, Julian (1916). A Treatise on the Circle and the Sphere. Oxford: Clarendon. (Internet Archive scan)
  • Gonick, Larry (2024). The Cartoon Guide to Geometry. William Morrow. ISBN 978-0-06-315757-6. An axiomatic treatment of high-school geometry.
  • Gonick, Larry (2011). The Cartoon Guide to Calculus. William Morrow. ISBN 978-0-06-168909-3. Called "an excellent treatment" by MAA Reviews [1].
  • Moebs, William; et al. (2024). University Physics. Vol. 1 (digital ed.). OpenStax. ISBN 978-1-947172-20-3. Probably as good as any textbook for the basics of circular motion.
  • O'Connor, John J.; Robertson, Edmund F., "Circle", MacTutor History of Mathematics Archive, University of St Andrews
  • O'Connor, John J.; Robertson, Edmund F., "Squaring the circle", MacTutor History of Mathematics Archive, University of St Andrews
  • Sidoli, Nathan; Thomas, Robert Spencer David, eds. (2023). The Spherics of Theodosios. London: Routledge. doi:10.4324/9781003142164. ISBN 0-367-55730-4.
  • "Geometry and Trigonometry textbooks". Open Textbook Library. University of New Mexico.
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