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
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Author AnonMoos
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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:
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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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