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

1DLine, Circular Arc, Parabola, Helix, Koch Curve
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, 1/2 EL Triangle, Quadrilateral, Rectangle, Golden Rectangle, Rhombus, Parallelogram, Kite, 60-90-120 Kite, Half Square Kite, Right Kite, Trapezoid, Right Trapezoid, Isosceles Trapezoid, Tri-equilateral Trapezoid, Obtuse Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Concave Quadrilateral, Crossed Rectangle, Antiparallelogram, House-Shape, Symmetric Pentagon, Diagonally Bisected Octagon, Cut Rectangle, Concave Pentagon, Concave Regular Pentagon, Stretched Pentagon, Straight Bisected Octagon, Stretched Hexagon, Symmetric Hexagon, Semi-regular Hexagon, Parallelogon, Concave Hexagon, Arrow-Hexagon, Rectangular Hexagon, L-Shape, Sharp Kink, T-Shape, Square Heptagon, Truncated Square, Stretched Octagon, Frame, Open Frame, Grid, Cross, X-Shape, H-Shape, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Double Star Polygon, Polygram, The Hat, 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, Two Circles, Lancet Arch, Knoll, Annulus, Semi-Annulus, Annulus Sector, Annulus Segment, Cash, Curved Rectangle, Rounded Polygon, Rounded Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Elliptical Ring, Stadium, Spiral, Log. Spiral, Reuleaux Triangle, Cycloid, Double Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Heart, Tricorn, Interarc Triangle, Circular Arc Triangle, Interarc Quadrangle, Intercircle Quadrangle, Circular Arc Quadrangle, Circular Arc Polygon, Claw, Half Yin-Yang, Arbelos, Salinon, Bulge, Lune, Three Circles, Polycircle, Round-Edged Polygon, Rose, Gear, Oval, Egg-Profile, Lemniscate, Squircle, Circular Square, 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, Square Frustum, Regular Frustum, Frustum, Bent Pyramid, Regular Bipyramid, Bipyramid, Bifrustum, Frustum-Pyramid, Ramp, Right Wedge, Wedge, Half Tetrahedron, Rhombohedron, Parallelepiped, Regular Prism, Prism, Oblique Prism, Anticube, 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, Elongated Dodecahedron, Truncated Rhombohedron, Obelisk, Bent Cuboid, 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, Elliptic Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Truncated Elliptic Cone, General Cone, General Truncated Cone, Bicone, Truncated Bicone, Pointed Pillar, Rounded Cone, Drop, Spheroid, Ellipsoid, Semi-Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Central Segment, Double Calotte, Double Sphere, Spherical Wedge, Half Cylinder, Diagonally Halved Cylinder, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Half Cone, Conical Sector, Conical Wedge, Spherical Shell, Half Spherical Shell, Spherical Shell Cap, 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, Capsule Segment, Double Point, Anticone, Truncated Anticone, Sphere-Cylinder, Lens, Concave Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids, Solid of Revolution
4D Tesseract, Hypersphere


Koch Curve Calculator

Calculations at a Koch curve. The Koch curve is built by dividing a line into three equal segments, putting an equilateral triangle above the middle segment and removing the bottom line of this. This is repeated with the four new lines, and so on, infinitely. This makes the Koch curve a fractal with the Hausdorff dimension ln(4)/ln(3)≈1,26186 and infinite length.
The single steps are called iterations. Here, the length of a Koch curve after n iterations can be calculated. Its height is the height of the first equilateral triangle.
Enter the number of iterations and one of the two lengths. Choose the number of decimal places, then click Calculate.

Helge von Koch Number of iterations (n): Koch curve
Koch curve with n=3
Original line length (l):
Length after n iterations (m):
Height (h):
Round to    decimal places.

m = l * (4/3)n
h = √3 / 6 * l

Lengths and height have the same one-dimensional unit (e.g. meter). The number of iterations is dimensionless and an integer.

The name fractal was Benoît by BenoĆ®t Mandelbrot, it comes from the Latin word fractus, which means broken. This refers to the Hausdorff dimension of such structures, which, unlike the geometric shapes we are used to, is not an integer. To calculate the Hausdorff dimension for the Koch curve, see above. If it is tripled in each direction, this curve becomes four times as large. A rectangle, for example, becomes nine, i.e. 3² times as large, if it is tripled in each direction, and is therefore two-dimensional. A cuboid, on the other hand, would be 27, i.e. 3³ times as large, and is therefore three-dimensional.
However, the famous Mandelbrot set named after Mandelbrot is also a fractal, although not only the set itself, but also its boundary line has the Hausdorff dimension 2, although it is not known whether the boundary has an area or not. But this is only a glimpse into the world of fractals, into which the Koch curve represents a good introduction.

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