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Book: GeometryTheorems

I am making a list of geometry theorems and sorting them by the geometry they presume.


Difference between stating a proof (final copy) as an element of a monoid, where no step is taken back, and exploratory thinking (rough draft) where ideas (suppositions) can be thought and rethought or even unthought.

Geometry theorems

Organized by Equivalence Types

Different ways of defining equivalence and thus distance:

Compare with types of poems!

Equivalent paths

Monoid - binomial theorem.

Weak n-categories.

Triangle == three vectors which, added together, take you back to where you started


Equivalent positions

Triangle == three lines such that each pair of lines intersects at a different point

Concurrency: line intersections


Functions of points

Singular sets

Incidence geometry, incidence structures, intersection theorem, block designs

Projective space

Homography, perspectivities

Equivalent angles - proportions - quotients

Triangle == angles add up to 180 degrees

Angle comparisons

Angles - proportions

Concurrency: line intersections (related to circles, conics, equilateral triangles...)

Collinearity (related to conics, equilateral triangle)

Points on a conic

Tangents to an oval

Circle intersections (based on angles?)

Equilateral triangles

Isosceles triangles



Equivalent areas - products

Triangle == sum of two right triangles & Right triangle == half of a rectangle

Calculating area


Minimal areas

Distance as areas

Assembling areas

Quadratic forms

N-dimensional volume



The probability distribution of a simplex (equilateral triangle) - the center must be 1/n. This same results holds for my arbitrary triangle and its center.

Parsiųstas iš http://www.ms.lt/sodas/Book/GeometryTheorems
Puslapis paskutinį kartą pakeistas 2016 gruodžio 01 d., 21:53