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Geometry | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner, Formen

  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, Golden Rectangle, Rhombus, Parallelogram, Half Square Kite, Right Kite, Kite, Right Trapezoid, Isosceles Trapezoid, Tri-equilateral Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Concave Quadrilateral, Crossed Rectangle, Antiparallelogram, House-Shape, Symmetric Pentagon, Cut Rectangle, Concave Pentagon, Concave Regular Pentagon, Parallelogon, Stretched Hexagon, Concave Hexagon, Arrow-Hexagon, L-Shape, Sharp Kink, T-Shape, Truncated Square, Frame, Cross, X-Shape, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Double Star Polygon, Polygram, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Circular Central Segment, Round Corner, Circular Corner, Circle Tangent Arrow, Drop Shape, 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, Heart, Tricorn, Interarc Triangle, Circular Arc Triangle, Circular Arc Quadrangle, Half Yin-Yang, 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, Bipyramids, Elongated Bipyramids, Gyroelongated Square Dipyramid, Gyrobifastigium, Disheptahedron, Snub Disphenoid, Sphenocorona, Disphenocingulum

Other Polyhedrons:
Cuboid, Square Pillar, Triangular Pyramid, Square Pyramid, Regular Pyramid, Pyramid, Regular Frustum, Frustum, Regular Bipyramid, Bipyramid, Bifrustum, Frustum-Pyramid, Ramp, Right Wedge, Wedge, Half Tetrahedron, Rhombohedron, Parallelepiped, Regular Prism, Prism, Oblique Prism, Antiprism, Prismatoid, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Wedge-Cuboid, Half Cuboid, Skewed Cuboid, Ingot, Skewed Three-Edged Prism, Cut Cuboid, Truncated Cuboid, Obtuse Edged Cuboid, Obelisk, Elongated Dodecahedron, Truncated Rhombohedron, Hollow Cuboid, Hollow Pyramid, Hollow Frustum, Star Pyramid, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Great Dodecahedron, Great Icosahedron

Round Forms:
Sphere, Hemisphere, Spherical Corner, Cylinder, Cut Cylinder, Oblique Cylinder, Bent Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Bicone, Truncated Bicone, Pointed Pillar, Rounded Cone, Drop, Spheroid, Ellipsoid, Semi-Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Central Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Conical Sector, Conical Wedge, Spherical Shell, Cylindrical Shell, Cut Cylindrical Shell, Oblique 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, Solid of Revolution
4D Tesseract, Hypersphere

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Logarithmic Spiral Calculator

Calculations at a logarithmic spiral. With this form of spirals, the radius increases proportionally with the spiral length. So the distance between two turnings increases with each turning for the factor f. The shape parameter determines the spiral's shape, this value mostly if far less than 1. It is easier to use the growth factor instead. The distance from the spiral start to the origin matches the size parameter a. Enter radius, number of revolutions or angle and shape parameter or growth factor. Choose the number of decimal places, then click Calculate. Please enter angles in degrees, here you can convert angle units.


Jacob Bernoulli, painted by Niklaus Bernoulli Spiral radius (r): Logarithmic Spiral with k = 0,19
A logarithmic spiral with 3 turnings and k = 0,19.
Number of turnings (n):
Angle (φ):
Shape parameter k:
Growth factor f:
Size parameter a:
Spiral length (l):
Outer perimeter (p):
Diameter (d):
Height (h):
Osculating radius (ρ):
Area (A):
Round to    decimal places.



Formulas:
r = a * ek*φ
n = φ / 360°
f = ( e2π )k
l = ( r - a ) / sin( arctan(k) )
p = l + r for n≤1
p = r - a * ek*(φ-360°) + l - ( a * ek*(φ-360°) - a ) / sin( arctan(k) ) for n>1
d = r + a * ek*(φ-180°) for φ>180°
h = a * ( ek*(φ-90°) + ek*(φ-270°) ) für φ>270°
ρ = r / cos( arctan(k) )
A = ( r² - a² ) / (4k)

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, the shape parameter and the growth factor are dimensionless.




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