Simple 4-quadrant heart curve
Mathematically simple heart shape. Some have come up with advanced and complex algebraic or trigonometric equations to approximate the heart/love symbol. This image instead uses two simple perpendicular straight lines and two partial circular arcs. Mathematically, x and y are related by the following four equations (one applying in each quadrant):
- Ist quadrant (x≥0,y≥0)
- (x–3.3030615433)2+(y–2.6969384567)2=14.5469540784
- IInd quadrant (x≤0,y≥0)
- (x+3.3030615433)2+(y–2.6969384567)2=14.5469540784
- IIIrd quadrant (x≤0,y≤0)
- x+y= –6
- IVth quadrant (x≥0,y≤0)
- y–x= –6
Where the approximate constants in the first two equations have the following exact values:
- 14.5469540784=144/(√2+√3)2
- 3.3030615433=(√108)/(√2+√3)
- 2.6969384567=6–((√108)/(√2+√3))
(The first of these is the square of the radius of the circular arcs.)
There's a 90° corner at coordinate point (0,–6) and a 60° corner at (0,4.6039619279).
Where 4.6039619279=6(1–((√3–1)/(√2+√3)))
The width of the area enclosed by the curve is 14.2342169713=12((2+√3)/(√2+√3)), while the height is 12.510985399=12(1+((1–√.75)/(√2+√3)))![]() |
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