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File:Simple 4-quadrant heart curve.svg

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Description

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)))
Date
Source Own work
Author AnonMoos
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions

For images using this heart shape, see File:Heart-padlock.svg and related images.

Alternative mathematically-defined heart shapes:

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30 July 2014

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Date/TimeThumbnailDimensionsUserComment
current08:10, 31 July 2014Thumbnail for version as of 08:10, 31 July 2014625 × 600 (2 KB)AnonMoos{{Information |Description=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 straight lines and partial circula...

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