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  1D Line
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, Right Kite, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Symmetric Pentagon, Concave Pentagon, Parallelogon, Sharp Kink, Frame, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Curved Rectangle, Ellipse, Semi-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, Pentagonal Icositetrahedron

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, Hollow Cuboid, 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, Semi-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
4D Tesseract, Hypersphere


Lens Calculator

Calculations in a convex spherical lens. This is made of two spherical caps, in between a cylinder. Those three have equal sized circular areas with the radius rc. The focal length of a lense depends on its refractive index, which is determined by its material. Here, 1.5 is set, the value for normal glass. Enter both sphere radiuses and the cylinder radius and choose the number of decimal places. Then click Calculate. The cylinder height can also be 0.

Galileo Galilei, by Justus Sustermans Radius first sphere (r1): Lens
Radius second sphere (r2):
Cylinder radius (rc):
Cylinder height (hc):
Refractive index (n):
Height of the first spherical cap (h1):
Height of the second spherical cap (h2):
Height of the lense (h):
Focal length (f):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.

h1 = ( 2 * r1 - √ 4r1² - 4rc² ) / 2
h2 = ( 2 * r2 - √ 4r2² - 4rc² ) / 2
h = h1 + h2 + hc
f = 1 / { (n-1) * [ 1/r1 + 1/r2 - h*(n-1)/(n*r1*r2) ] }
A = 2 * π * ( r1 * h1 + r2 * h2 + rc * hc )
V = π/3 * [ h1² * ( 3 * r1 - h1 ) + h2² * ( 3 * r2 - h2 ) ] + π * rc² * hc

π = 3.141592653589793...

The refractive index has no unit, radius, heights and focal length have the same unit (e.g. centimeter), the area has this unit squared (e.g. square centimeter), the volume has this unit to the power of three (e.g. cubic centimeter). A/V has this unit -1.



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