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Formal definition of trigonometric functions

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#geometry #trigonometry #euclidean-geometry #axiomatic-geometry
801
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Equivalence relation between vectors in Euclidean geometry

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#geometry #euclidean-geometry #axiomatic-geometry
165
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Categorical axiomatization of projective spaces

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#reference-request #projective-space #axiomatic-geometry
256
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Axiomatic geometry - How do you define the measurement of lengths, areas, angles, etc.?

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#axiomatic-geometry
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Do we have to define natural numbers in geometry?

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#definition #axiomatic-geometry
139
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Axioms of one-dimension geometry in Hilbert's style

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#geometry #foundations #axiomatic-geometry
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Can we really intersect circles?

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#circles #foundations #axiomatic-geometry
106
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Saccheri quadrilaterals in Hartshorne's "Euclid and Beyond"

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#euclidean-geometry #axiomatic-geometry
96
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What kind of curves can be defined in euclidean geometry?

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#logic #euclidean-geometry #analytic-geometry #axiomatic-geometry
184
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How did Pasch show his axiom was independent of Euclid's?

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#geometry #logic #reference-request #axiomatic-geometry
117
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Are Pasch's axiom and plane separation postulate equivalent?

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#geometry #logic #noneuclidean-geometry #axiomatic-geometry
150
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Do Tarski's axioms apply to higher dimensions?

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#euclidean-geometry #foundations #meta-math #formal-systems #axiomatic-geometry
44
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Pasch's axiom, intermediate value theorem and Jordan curve theorem

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#euclidean-geometry #axioms #axiomatic-geometry
196
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Does the Axiom of Constructibility make Pasch's Axiom unnecessary?

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#geometry #logic #model-theory #constructive-mathematics #axiomatic-geometry
111
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Prove that the radius of the incircle of one triangle has two times the radius of the incircle of another triangle with Euclidean geometry.

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#euclidean-geometry #triangles #circles #axiomatic-geometry

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