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ceptred
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There are 7 letters in CEPTRED ( C3D2E1P3R1T1 )
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Ceptred might refer to |
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In geometry, a Centered trochoid is the roulette formed by a circle rolling along another circle. That is, it is the path traced by a point attached to a circle as the circle rolls without slipping along a fixed circle. The term encompasses both epitrochoid and hypotrochoid. The center of this curve is defined to be the center of the fixed circle. * Alternatively, a centered trochoid can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle. Specifically, a centered trochoid is a curve that can be parameterized in the complex plane by* * * * z * = * * r * * 1 * * * * e * * i * * ω * * 1 * * * t * * * + * * r * * 2 * * * * e * * i * * ω * * 2 * * * t * * * , * * * * {\displaystyle z=r_{1}e^{i\omega _{1}t}+r_{2}e^{i\omega _{2}t},\,} * or in the Cartesian plane by * * * * * x * = * * r * * 1 * * * cos * * ( * * ω * * 1 * * * t * ) * + * * r * * 2 * * * cos * * ( * * ω * * 2 * * * t * ) * , * * * {\displaystyle x=r_{1}\cos(\omega _{1}t)+r_{2}\cos(\omega _{2}t),} * * * * * * y * = * * r * * 1 * * * sin * * ( * * ω * * 1 * * * t * ) * + * * r * * 2 * * * sin * * ( * * ω * * 2 * * * t * ) * , * * * * {\displaystyle y=r_{1}\sin(\omega _{1}t)+r_{2}\sin(\omega _{2}t),\,} * where * * * * * * r * * 1 * * * , * * r * * 2 * * * , * * ω * * 1 * * * , * * ω * * 2 * * * ≠ * 0 * , * * * ω * * 1 * * * ≠ * * ω * * 2 * * * . * * * * {\displaystyle r_{1},r_{2},\omega _{1},\omega _{2}\neq 0,\quad \omega _{1}\neq \omega _{2}.\,} * If * * * * * ω * * 1 * ... |