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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Length times width e.g.
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Hint 1 meaning
The superficial contents of any figure; the surface included
within any given lines; superficial extent; as, the area of a square or
a triangle.
Hint 2 anagram
ERAA
Hint 3 another clue
CERTAIN BRAIN SIZE
33 +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.