"SERIES, ARC LENGTH (CIRCUMFERENCE) OF ELLIPSE. The arc length or circumference of an ellipse can be written in a series: ■ 1 (a-b) 2 1 (a-b) 4 1 (a-b) 6 L = pi (a+b) [ 1 + ─ (─────) + ── (─────) + ──── (─────) + ..... 4 (a+b) 64 (a+b) 256 (a+b) ■ where a and b are 1/2 the lengths of the two principal axes. The recursive term of this series is written as a function of the index N and is shown below. To estimate the circumference, sum on N from N=0 to N=6. (c) Copyright PCSCC, Inc., 1993*** Answer(s) to problem *** Set A=50 and B=10. Move cursor to N. Type @G ( @ first then G next). For the range on index N type, (end esc) 0 to 6 (enter). The circumference is approximately 210.0285 using the first 7 terms. Type any key to exit. ||Estimate the circumference of an ellipse with axes lengths of 50 and 10 cm as measured from its origin. Use the series approximation. Type comma key to see answer. Type (F2) to return to application file."
