Calculations at a simple bulge shape. This is made from a semicircle, on which ends an outward bound quarter circle with the same radius is attached and the new ends are connected.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
pi:
Length, width, height and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The perimeter of this bulge shape is that of the sphere plus the bottom straight line with the length b. Its area is equal to that of a square with a side length of 2r, into which the shape can be reassembled after a dissection.
The bulge is a non-convex shape because the outwardly curved quarter-circles are concave. Such a bulge is a method of creating a smooth transition from a sphere to a straight line. This shape, which has a straight side at the ends of the outward bound circular arcs, has two corners there, each with an angle of zero degrees. Such angles are possible with curved sides.
This shape is axially symmetric about its perpendicular bisector. It possesses no other symmetries. While the term perpendicular bisector is typically used in the context of straight lines, it is employed here in an extended sense. This perpendicular bisector is perpendicular to the straight side, bisecting it at its midpoint, and also intersects the hemisphere perpendicularly, bisecting it as well.
A steeper or flatter bulge can be created by using an ellipse instead of a circle as the initial shape and then bending its two lower quarters outward. The term bulge is likely associated more with a flatter shape, which is an ellipse divided along its major axis.
Bulge is not a formal geometric term. It was chosen here because it describes this two-dimensional shape quite well. A three-dimensional shape could also be called a bulge, This could be, for instance, the solid of revolution formed by rotating this shape around its perpendicular bisector. This would result in a hemisphere as the upper section and, as the lower section, a cylinder from which a toroid based on a quarter-circle profile has been removed, half an inner semicircle toroid.