Calculations at a geometric simple heart shape. This heart is based on a square standing on one tip. On each of its upper two sides, a matching semicircle is attached. So it consists of a square and a circle, where the diameter of the circle is equal to the side length of the square.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
b = ( √2 / 2 + 1 ) * a
h = ( 3/4 * √2 + 1/2 ) * a
p = ( 2 + π ) * a
A = ( 1 + π / 4 ) * a²
pi:
π = 3.141592653589793...
Length, width, height and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
Hearts are usually depicted a little differently, and their shape is usually more complicated than this one. The upper, concave tip, which points inwards, is often cut deeper. However, a shape based on a square and a circle is easy to calculate and is therefore used here. Other heart shapes often do not contain any straight lines and the curves are not circular. At best, these are based on other geometric bodies whose shape and calculation are known, and then you can work with them in the same way. If the curves that make up the heart can be represented as mathematical functions, you have to work with integrals to calculate the area and circumference, which can be very demanding. Calculating the circumference is often even more difficult than calculating the area. Terms based on trigonometric functions such as sine and tangent and based on roots could possibly describe such curves. Sometimes there is no geometric solution for these integrals, as is the case with the circumference of an ellipse, for example. What at least most graphic hearts have in common is a convex tip at the bottom and a concave tip at the top and their axial symmetry to the straight line through these two tips.