Crossword-Solution: HYPOCYCLOID
Dictionary
| Word | Word Type | Definition |
|---|---|---|
| Hypocycloid | n. | A curve traced by a point in the circumference of a circle which rolls on the concave side in the fixed circle. Cf. Epicycloid, and Trochoid. |
We have 2 clues for the answer “HYPOCYCLOID”
| Clue | Answers |
|---|---|
| roulette | 5 answers |
| Curve | 60 answers |
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Dermatological complaint
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Hint 1 meaning
An inflammatory disease of the skin, characterized by the
presence of redness and itching, an eruption of small vesicles, and the
discharge of a watery exudation, which often dries up, leaving the skin
covered with crusts; -- called also tetter, milk crust, and salt rheum.
Hint 2 anagram
CEZMEA
Hint 3 another clue
eruption
12 +2
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Sentences with HYPOCYCLOID (5)
Take in succession as radii the chords A 1, A 2, A 3, etc., of the describing circle, and with centres 1, 2, 3, etc., on the base circle, strike arcs either externally or internally, as shown respectively on the right and left; the curve tangent to the external arcs is the epicycloid, that tangent to the internal ones the hypocycloid, forming the face and flank of a tooth for the base circle.
The curve traced by a point in the circumference of the rolling circle when it rolls on the concave side of a fixed circle is called a hypocycloid; the curve traced by a point rigidly connected with the rolling circle in this case, but not its circumference, is called a hypotrochoid.
Leonhard Euler (_Acta Petrop._ 1784) showed that the same hypocycloid can be generated by circles having radii of ½(a ± b) rolling on a circle of radius a; and also that the hypocycloid formed when the radius of the rolling circle is greater than that of the fixed circle is the same as the epicycloid formed by the rolling of a circle whose radius is the difference of the original radii.
Therefore any epicycloid or hypocycloid may be represented by the equations p = A sin B[psi] or p = A cos B[psi], s = A sin B[psi] or s = A cos B[psi], or r² = A + Bp², the constants A and B being readily determined by the above considerations.
But the minimum of friction is attained when the two flanks for the tooth are drawn into one common hypocycloid, as in Fig.