1D Line
2D
Regular Polygons: Equilateral Triangle , Square , Pentagon , Hexagon , Heptagon , Octagon , Nonagon , Decagon , Hendecagon , Dodecagon , Hexadecagon , N-gon , Polygon Ring
Other Polygons: Triangle , Right Triangle , Isosceles Triangle , IR Triangle , Quadrilateral , Rectangle , Rhombus , Parallelogram , Half Square Kite , Right Kite , Kite , Right Trapezoid , Isosceles Trapezoid , Trapezoid , Cyclic Quadrilateral , Tangential Quadrilateral , Arrowhead , Concave Quadrilateral , Antiparallelogram , House-Shape , Symmetric Pentagon , Concave Pentagon , Parallelogon , Stretched Hexagon , Arrow-Hexagon , L-Shape , Sharp Kink , Truncated Square , Frame , Threestar , Fourstar , Pentagram , Hexagram , Unicursal Hexagram , Cross , Oktagram , Star of Lakshmi , Polygram , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Round Corner , Circular Corner , Crescent , Pointed Oval , Lancet Arch , Knoll , Annulus , Annulus Sector , Curved Rectangle , Rounded Polygon , Rounded Rectangle , Ellipse , Semi-Ellipse , Elliptical Segment , Elliptical Sector , Elliptical Ring , Stadium , Spiral , Log. Spiral , Reuleaux Triangle , Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Tricorn , Arbelos , Salinon , Lune , Three Circles , Polycircle , Round-Edged Polygon , Rose , Gear , Oval , Egg-Profile , Lemniscate , Squircle , Digon , Spherical Triangle
3D
Platonic Solids: Tetrahedron , Cube , Octahedron , Dodecahedron , Icosahedron
Archimedean Solids: Truncated Tetrahedron , Cuboctahedron , Truncated Cube , Truncated Octahedron , Rhombicuboctahedron , Truncated Cuboctahedron , Icosidodecahedron , Truncated Dodecahedron , Truncated Icosahedron , Snub Cube , Rhombicosidodecahedron , Truncated Icosidodecahedron , Snub Dodecahedron
Catalan Solids: Triakis Tetrahedron , Rhombic Dodecahedron , Triakis Octahedron , Tetrakis Hexahedron , Deltoidal Icositetrahedron , Hexakis Octahedron , Rhombic Triacontahedron , Triakis Icosahedron , Pentakis Dodecahedron , Pentagonal Icositetrahedron , Deltoidal Hexecontahedron , Hexakis Icosahedron , Pentagonal Hexecontahedron
Johnson Solids: Pyramids , Cupolae , Rotunda , Elongated Pyramids , Gyroelongated Pyramids , Elongated Bipyramids , Disheptahedron , Snub Disphenoid , Sphenocorona , Disphenocingulum
Other Polyhedrons: Cuboid , Square Pillar , Triangular Pyramid , 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 , Wedge-Cuboid , Half Cuboid , Skewed Cuboid , Skewed Three-Edged Prism , Obtuse Edged Cuboid , Elongated Dodecahedron , Truncated Rhombohedron , Hollow Cuboid , Hollow Pyramid , Hollow Frustum , Stellated Octahedron , Small Stellated Dodecahedron , Great Stellated Dodecahedron
Round Forms: Sphere , Hemisphere , Spherical Corner , Cylinder , Cut Cylinder , Oblique Cylinder , Generalized Cylinder , Cone , Truncated Cone , Oblique Circular Cone , Elliptic Cone , Bicone , Truncated Bicone , Rounded Cone , Spheroid , Ellipsoid , Semi-Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Wedge , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Conical Sector , Conical Wedge , Spherical Shell , Cylindrical Shell , Hollow Cone , Truncated Hollow Cone , Spherical Ring , Torus , Spindle Torus , Toroid , Torus Sector , Toroid Sector , Arch , Reuleaux-Tetrahedron , Capsule , Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids
4D
Tesseract , Hypersphere
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Gear Calculator
Calculations in a gear, or cogwheel, with isosceles trapezoids as cogs. Those are set regularly on a circle , so that the cog edge exactly fits in the gap between the cogs. This is a simplified representation of a gear, it is not checked whether the gear works or not. For a gear with pointed cogs, see polygram .
The required input is: for the number of cogs a natural number of at least 3. Two values of circle radius, cog height and gear radius. The ratio between cog edge (or gap) and cog base. For this, v ∈ ] 0 ; 1 [ must apply. The other values will be calculated.

Formulas:
R = r + i
a = 2 * π * r / [ n * ( 1 + 1/v ) ]
b = a / v
h = r * { 1 - cos[b/(2r)] } + i
c = √ h² + (a-b)² / 4
s = 2 * √ 2 * r * (h-i) - (h-i)²
p = 2n * (a + c)
A = π * r² + n/2 * [ √ ( a + b )² * ( a - b + 2c ) * ( b - a + 2c ) / 2 - r * b + s * ( r - h + i ) ]
Test, if c intersects the circle:
if b/(2r) > arccos{ [ (s-a)²/4 + c² - h² ] / [ (s-a) * c ] }
the cog is too flat.
pi:
π = 3.141592653589793...

Radiuses, heights, lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

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