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2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, N-gon

Other Polygons:
Triangle, Right Triangle, Isosceles Triangle, IR Triangle, Quadrilateral, Rectangle, Rhombus, Parallelogram, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Concave Pentagon, Parallelogon, Threestar, Fourstar, Pentagram, Hexagram, Oktagram, Star of Lakshmi

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Ellipse, Elliptical Segment, Stadium, Digon, Spherical Triangle, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Parabolic Segment, Arbelos, Salinon, Lune, Oval, Three Circles, Lemniscate, Squircle
3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

Archimedean Solids:
Truncated Tetrahedron, Cuboctahedron, Truncated Cube, Truncated Octahedron, Rhombicuboctahedron, Icosidodecahedron, Truncated Dodecahedron, Truncated Icosahedron

Catalan Solids:
Triakis Tetrahedron, Rhombic Dodecahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Rhombic Triacontahedron

Johnson Solids:
Pyramids, Cupolae, Rotunda, Elongated Pyramids, Snub Disphenoid

Other Polyhedrons:
Cuboid, Square Pillar, Square Pyramid, Regular Pyramid, Pyramid, Regular Frustum, Frustum, Bipyramid, Ramp, Right Wedge, Wedge, Rhombohedron, Parallelepiped, Prism, Oblique Prism, Antiprism, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Half Cuboid, Truncated Rhombohedron, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron

Round Forms:
Sphere, Hemisphere, Cylinder, Cut Cylinder, Oblique Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Spheroid, Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Spherical Shell, Cylindrical Shell, Spherical Ring, Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


Oval Calculator

Calculations in an oval. An oval is mathematically elusive, the word means egg-shaped. Usually, an oval is seen as a round, convex shape without vertex and with one symmetry axis. This special oval is formed by two circles with radiuses R and r and a distance a of their centers. Around both circles, a third one is laid, which touches each of them in one point. The center of this is at the intersection of the two lines through touch points and centers of the other two circles. The area formed by this, a flat projection of a spherical triangle, is added to the two circles. This is repeated on the other side of both circles.

Albrecht Dürer Radius large circle (R): Oval
Radius small circle (r):
Distance of the centers (a):
Radius joining circle (ρ):
Area (A):
Round to    decimal places.

Oval construction
Construction of an oval.


ρ = ( a² + R² - r² ) / [ 2 * ( R - r ) ]

A = 1/2 * { a(R-r) + π(r²+R²) - a³/(R-r) + [a²+(R-r)²] * (a²-3r²+2rR+R²) / [ 2 * ( R - r )² ] * arctan[ (2a(R-r)) / (a²-(R-r)²) ] }

If a ≤ R - r: A = π * R²
(identical to a circle with radius R, there is no joining circle)

If R = r: ρ=∞, A = π * R² + 2 * a * R
(identical to a stadium with circle radius R and rectangle length a)

Source: Weisstein, Eric W. From MathWorld--A Wolfram Web Resource.

π = 3.141592653589793...

Radiuses and distance have a one-dimensional unit (e.g. meter), the area has this unit squared (e.g. square meter).



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