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 , 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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Archimedean Spiral Calculator
Calculations in an archimedean or arithmetic spiral. This is the simplest form of spirals, where the radius increases proportionally with the angle. The radius is the distance from the center to the end of the spiral. Enter radius and number of turnings or angle. Choose the number of decimal places, then click Calculate. Please enter angles in degrees, here you can convert angle units . The surface area of the archimedean spiral can only be calculated if the number of turnings is an integer.

Formulas:
r = a * φ

n = φ / 360°

r

_{1} = a * 360° = r / n

l = a / 2 * [ φ * √

1 + φ² + ln( φ + √

1 + φ² ) ]

p = l(φ) + r for n≤1

p = l(φ) - l(φ-360°) + r

_{1} for n>1

d = a * φ + a * (φ-180°) for φ>180°

κ = ( φ² + 2) / [ a * ( φ² + 1)

^{3/2} ]

n
A = 4/3 π³ a² + Σ 8 ( i - 1 ) π³ a²
i=2

Σ is the

sum symbol ,

ln is the logarithmus naturalis (natural logarithm).

pi:

π = 3.141592653589793...

Radius, parameter a, length, perimeter and diameter have a one-dimensional unit (e.g. meter), the area has this unit squared (e.g. square meter). The number of turnings is dimensionless. The unit of the curvature is 1 / length unit.

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