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prettygoodwordcardioid (KAHR-dee-oid) - n., a somewhat heart-shaped planar curve, being the path of a point on a circle that rolls externally, without slipping, on another equal circle.
Here's a GIF of the rolling, the red part being the cardiod:
Thanks, WikiMedia!
Can also be, in a more shorthand way, defined as an epicycloid with exactly one cusp. Or even more briefly with the equation ρ = 2a (1 - cos θ) in polar coordinates or x = a cos θ (1 - cos θ),
y = a sin θ (1 - cos θ) in Cartesian coordinates, where a is the ratio of the radii of the two circles. Name was coined in 1741 by Italian mathematician Giovanni Salvemini di Castiglione from Ancient Greek kardioeidḗs, heart-shaped.
---L.
Here's a GIF of the rolling, the red part being the cardiod:
Thanks, WikiMedia!
Can also be, in a more shorthand way, defined as an epicycloid with exactly one cusp. Or even more briefly with the equation ρ = 2a (1 - cos θ) in polar coordinates or x = a cos θ (1 - cos θ),
y = a sin θ (1 - cos θ) in Cartesian coordinates, where a is the ratio of the radii of the two circles. Name was coined in 1741 by Italian mathematician Giovanni Salvemini di Castiglione from Ancient Greek kardioeidḗs, heart-shaped.
---L.
