

  1D Line
2D Regular Polygons:

Other Polygons:

Round Forms:
3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

Archimedean Solids:

Catalan Solids:

Johnson Solids:

Other Polyhedrons:

Round Forms:
4D Tesseract, Hypersphere


Knoll Calculator

Calculations in a knoll. Here, a knoll is an isosceles trapezoid with a matching circular segment attached in a way, so that at the connection between trapezoid and segment no vertex will appear. Enter the three trapezoid lengths, choose the number of decimal places and click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units. The angle of the circular segment Θ = 2α.

Euclid Longer side (a): Knoll
Shorter side (b):
Legs (c):
Knoll angle (α):
Circular segment height (i):
Trapezoid height (j):
Knoll height (h):
Arc length (l):
Perimeter (p):
Area (A):
Round to    decimal places.

j = 1/2 * √ 4c² - ( a - b )²
α = arccos{ [ ((a-b)/2)² + c² - j² ] / [ (a-b) * c ] }
i = √ b²/4 / [ 2 / ( 1 - cos α ) - 1 ]
h = i + j
l = i * 2α / ( 1 - cos α )
p = a + 2c + l
A = √ ( a + b )² * ( a - b + 2c ) * ( b - a + 2c ) / 4 + l² / ( 4 α ) - b * [ l / ( 2 α ) - i ] / 2

(α in rad)




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