Invertible Valentine heart
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A special heart that inverts to the identical shape upside down. Magic angle = arctan(π/2)
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Model information
- Source
- Printables
- Category
- Math
- License
- Creative Commons — Attribution
PRINTING: Use vase mode with zero bottom layers.
When making an invertible curve, it is natural to try and predict what the curve will look like inside out. And besides the circle, the results are often surprising.
But what curves besides the circle invert to themselves?
The classic heart shape comes pretty close to working, but fails because the length of the straight side does not match the length of the curved side. Also, the angle between the circular arcs needs to match the angle between the straight sides.
It turns out that the angle of arctan(π/2) create a triangle whose adjacent side length matched the length of a semicircle placed on the opposite side length.
The model and its inverse are incredibly close and can really only be differentiated by the amount of tension in the heart.