2D
Regular Polygons: Equilateral Triangle , Square , Pentagon , Hexagon , Heptagon , Octagon , Nonagon , Decagon , Hendecagon , Dodecagon , Hexadecagon , 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 , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Round Corner , Annulus , Annulus Sector , Curved Rectangle , Ellipse , Elliptical Segment , Elliptical Sector , Stadium , Digon , Spherical Triangle , Spiral , Log. Spiral , Reuleaux Triangle , Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Arbelos , Salinon , Lune , Three Circles , Oval , 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 , Snub Cube
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 , Bifrustum , Ramp , Right Wedge , Wedge , Rhombohedron , Parallelepiped , Prism , Oblique Prism , Antiprism , Prismatoid , Trapezohedron , Disphenoid , Corner , General Tetrahedron , Half Cuboid , Skewed Cuboid , Skewed Three-Edged Prism , 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 , Bicone , Spheroid , Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Wedge , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Spherical Shell , Cylindrical Shell , Spherical Ring , Torus , Arch , Reuleaux-Tetrahedron , Capsule , Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids
Anzeige

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.

Formulas:
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.

http://mathworld.wolfram.com/Oval.html
pi:
π = 3.141592653589793...

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

Anzeige

Share:

©

Jumk.de Webprojects
Anzeige