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507143
Caption: Pappus's theorem proved the formula for the volume of the solid torus obtained by rotating the disk of radius a around line L
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 32.16 MB
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481191
Caption: The figure illustrates the equivalence of the Chinese complementary rectangles theorem and the Greek similar triangles theorem.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 17.36 MB
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480997
Caption: Visual demonstration of the Pythagorean theorem.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 20.75 MB
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481439
Caption: A demonstration of the fundamental theorem of similarity, showing that small and large triangles are similar.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 25.88 MB
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481136
Caption: Projective version of Euclid's fundamental theorem of similarity.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 29.31 MB
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481077
Caption: Euclid offered a demonstration of the Pythagorean theorem in his Elements, named the Windmill proof due to the figure's shape.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 13.19 MB
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481348
Caption: K4 is planar, as its vertices can connect without intersecting lines, while K5 is not planar, as it must use a third dimension.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 23.02 MB
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481230
Caption: A bipartite map contains 2 sets of points such that every vertex in one can be connected to every vertex in the other without intersecting paths.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 35.78 MB
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481508
Caption: For any hexagon in any conic section the three pairs of opposite sides intersect in points on a straight line when extended.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 11.94 MB
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481283
Caption: A Eulerian circuit is a path that traverses each edge exactly once such that the path begins and ends at the same vertex.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 38.26 MB
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481286
Caption: Thales of Miletus proof that for any chord AB in a circle, all of the angles subtended by points on the same semiarc are equal.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 41.86 MB
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481208
Caption: Pappus of Alexandria proved that the 3 points formed by the 6 lines connecting 2 sets of collinear points are also collinear.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 28.17 MB
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481506
Caption: Illustration of the three basic theorems that triangles are congruent: side-angle-side, angle-side-angle, and side-side-side.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 33.87 MB
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481078
Caption: K5 is not a planar graph, as there is no way to connect every vertex with edges in the plane such that no edges intersect.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 37.75 MB
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481549
Caption: Proposed drawing of Thales' rectangle, a proof that any angle inscribed in a semicircle is a right angle (90 degrees).
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 37.62 MB
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481327
Caption: Cavalieri's principle: solids are of equal volume if they are of equal height and matching area at corresponding cross sections.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 11.94 MB
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481435
Caption: Basic types of graphs: simple graph, multigraph, complete graph, graph with loop, and digraph.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 30.44 MB
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481200
Caption: Liu Hui's 'Tangram' proof that the sum of the squares on the sides of a right triangle equals the square on the hypotenuse.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 35.68 MB
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481298
Caption: Pascal proved that the 3 points formed by intersecting the 6 lines connecting any 6 distinct points on a circle are collinear.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 41.02 MB
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481148
Caption: Dudeney puzzle (K3,3 bipartite graph): the houses cannot connect to the separate utilities such that no service pipes intersect.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 33.25 MB
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481343
Caption: If a saddlepoint does not exist for a payoff matrix, a probabilistic strategy is optimal to maximize expected (average) rewards.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 41.86 MB