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The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
The hypocycloid is a special kind of hypotrochoid, which is a particular kind of roulette. A hypocycloid with three cusps is known as a deltoid. A hypocycloid curve with four cusps is known as an astroid. The hypocycloid with two "cusps" is a degenerate but still very interesting case, known as the Tusi couple.
Epicycloid: variant of a cycloid in which a circle rolls on the outside of another circle instead of a line. Hypotrochoid: generalization of a hypocycloid where the generating point may not be on the edge of the rolling circle. Epitrochoid: generalization of an epicycloid where the generating point may not be on the edge of the rolling circle.
Construction of a two-lobed cycloidal rotor. The red curve is an epicycloid and the blue curve is a hypocycloid. The smaller generating circles (red and blue) are one quarter the diameter of the larger generating circle (black). The rotor profile is the thick line. A three-lobed Roots blower (Open animation)
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
It's flu season right now, and the U.S. is in the midst of a wave that's straining hospitals. But not all influenza is the same. There are some notable differences between flu A and flu B strains ...
Flu A and flu B are the most common strains of the flu that circulate in humans. The U.S. is currently in the middle of flu season, with a high number of cases reported across the country. There ...
Related: What's the Difference Between High Elevation and Low Elevation Wines? The importance of the diurnal shift. The best warm-weather regions aren’t typically marked by unrelenting heat. A ...