Search results
Results from the WOW.Com Content Network
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. [1] The evolute of an involute is the original curve.
Tractrix with object initially at (4, 0). Suppose the object is placed at (a, 0) and the puller at the origin, so that a is the length of the pulling thread. (In the example shown to the right, the value of a is 4.)
In the case where the rolling curve is a line and the generator is a point on the line, the roulette is called an involute of the fixed curve. If the rolling curve is a circle and the fixed curve is a line then the roulette is a trochoid. If, in this case, the point lies on the circle then the roulette is a cycloid.
At sections of the curve with ′ > or ′ < the curve is an involute of its evolute. (In the diagram: The blue parabola is an involute of the red semicubic parabola, which is actually the evolute of the blue parabola.) Proof of the last property:
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.
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
In the complex plane a rotation of a point around point (origin) by an angle can be performed by the multiplication of point (complex number) by . Hence the Hence the rotation Φ 3 {\displaystyle \Phi _{3}} around point 3 a {\displaystyle 3a} by angle 2 φ {\displaystyle 2\varphi } is : z ↦ 3 a + ( z − 3 a ) e i 2 φ {\displaystyle :z ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us