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506739
Caption: Duality associates with the point P the line RS, and vice versa
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 24.74 MB
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481352
Caption: Proof that the area of a triangle = 1/2 base x height.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 27.02 MB
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481128
Caption: Several points are labeled in a two-dimensional graph, known as the Cartesian plane.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 25.88 MB
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506809
Caption: Illustration of a continuous and a discontinuous function
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 40.15 MB
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506983
Caption: The hyperbolic functions cosh x and sinh x
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 27.60 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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507095
Caption: A conchoid curve results from connecting points drawn at standard distance a from line LN on all lines extending from point P
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 30.44 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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481330
Caption: Representation of an ellipsoid, a closed surface such that its intersection with any plane will produce an ellipse or a circle.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 23.02 MB
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481518
Caption: Poseidonius measures the Earth c. 100 BC.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 15.28 MB
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481388
Caption: The figure shows part of the graph of the polynomial equation y = 3x4 - 16x3 + 6x2 + 24x + 1.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 25.88 MB
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481146
Caption: Quadrature of the lune.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 16.85 MB
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481031
Caption: Archimedes' method of angle trisection.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 13.03 MB
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507138
Caption: In following the circle around the Mobius band, the line L twists, and the lines cannot be made to point in the same direction
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 24.05 MB
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481401
Caption: The eccentricity of a conic section completely characterizes its shape.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 41.86 MB
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481250
Caption: The normal, or perpendicular, at each point of a surface defines the corresponding tangent plane, and vice versa.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 31.59 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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481478
Caption: Proof, attributed to the Pythagoreans, that the sum of the angles in a triangle is 180 degrees.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 20.17 MB
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481443
Caption: The pseudosphere has constant negative curvature; it tapers to infinity in both directions away from the central disk.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 15.36 MB
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481375
Caption: Although distances and ratios of distances are not, the cross ratio, defined as AC/BC BD/AD, is preserved under projection.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 25.31 MB
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506949
Caption: Pappus of Alexandria (c 320) discovered that a hyperbola could be used to trisect an acute angle
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 17.32 MB
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481048
Caption: Medieval Arabic method of measuring the Earth.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 15.28 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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507066
Caption: In the Mandelbrot set, points remaining finite through all iterations are white Values diverging to infinity are shown darker
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 17.09 MB
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481183
Caption: Demonstration that an intrinsically straight line (the red line) is not necessarily the shortest distance between two points.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 39.19 MB
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481178
Caption: The curvature at each point of a line is 1/r (r = radius of the osculating circle best approximating the line at that point).
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 16.75 MB
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481493
Caption: Eratosthenes' knowledge of the sun's position and distance between points enabled him to calculate the Earth's circumference.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 15.28 MB
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506848
Caption: A Sierpinski gasket is made by dividing an equilateral triangle into four, removing the middle one, and repeating the pattern
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 36.54 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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481351
Caption: Quadrilateral of Omar Khayyam, constructed in an effort to prove Euclid's postulate concerning parallel lines superfluous.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 18.10 MB
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506663
Caption: Uniformly accelerated motion; s = speed, a = acceleration, t = time, and v = velocity
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 18.46 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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481311
Caption: Part of the elliptic paraboloid z = x2 + y2 which can be generated by rotating the parabola z = x2 (or z = y2) about the z-axis.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 38.70 MB
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506622
Caption: Standard lettering of a triangle: angles (A, B, C), sides (a, b, c), and one of the three heights (h, drawn from a vertices)
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 24.86 MB
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481282
Caption: Pierre de Fermat anticipated the calculus with his approach to finding the tangent line to a given curve.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 16.58 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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481450
Caption: The conic sections can be generated by projecting the circle formed by the intersection of a cone with the reality plane perpendicular to the cone's central axis.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 38.40 MB
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507004
Caption: Nicomedes (3rd century BCE) discovered a special curve, known as a conchoid, with which he was able to trisect any acute angle
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 31.01 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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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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481413
Caption: An example of a hyperbolic paraboloid. The figure shows part of the hyperbolic paraboloid x2/a2 - y2/b2 = 2cz.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 41.29 MB
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481087
Caption: An annular strip (region between two concentric circles) cut and bent into a helical strake following the contour of a cylinder.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 31.59 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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481001
Caption: Euclid's proposition that the base angles in an isosceles triangle are equal may have been named the Bridge of Asses.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 16.84 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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506842
Caption: Archimedes discovered that any sphere has two-thirds the surface area of its circumscribing cylinder
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 16.15 MB
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481057
Caption: The eye connects to points on the reality plane by sight lines that intersect with the picture plane, generating the drawing.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 29.31 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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481437
Caption: The ancient Greeks arranged pebbles in patterns to discern arithmetical, as well as mystical, relationships between numbers.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 18.60 MB
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481021
Caption: Each point on the Riemann sphere corresponds to a point on the plane. The ray tangent to the north pole corresponds to infinity.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 27.60 MB
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506691
Caption: In Ptolemy's geocentric model of the universe, the Sun, Moon, and each planet orbit a stationary Earth
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 36.84 MB
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507088
Caption: In Ptolemy's geocentric model of the universe, the Sun, Moon, and each planet orbit a stationary Earth
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 18.60 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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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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481267
Caption: Three models of hyperbolic geometry: the Klein-Beltrami model, the Poincare disk model, and the Poincare upper half-plane model.
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 36.16 MB
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480987
Caption: Satellite dish shaped like a portion of a paraboloid in order to focus transmission signals onto the pickup receiver (feedhorn).
Artist: Encyclopaedia Britannica
Release: Not Applicable
File Size: 33.99 MB