Simple 4-quadrant heart curve


Författare/Upphovsman:
AnonMoos
Kreditera:
Eget arbete
Upplösning:
625 x 600 Pixel (1941 Bytes)
Beskrivning:

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)))
Licens:
Public domain
Licenskommentaren:
Public domain Jag, upphovsrättsinnehavaren till detta verk, släpper detta verk i public domain. Detta gäller globalt.
I vissa länder kan detta inte vara juridiskt möjligt; i så fall:
Jag ger härmed envar rätten att använda detta verk för alla ändamål, utan några villkor, förutom villkor som lagen ställer.

Mer information om licensen för bilden finns här. Senaste uppdateringen: Fri, 29 Sep 2023 04:57:10 GMT