Area of a circle "ds" over the whole circle formula_33 is just the arc length, which is its circumference, so this shows that the area "A" enclosed by the circle is equal to formula_34 times the circumference of the circle. Note that the area of a semicircle of radius r can be computed by the integral formula_35. By trigonometric substitution, we substitute formula_36, hence formula_37 The last step follows since the trigonometric identity formula_42 implies that formula_43 and formula_44 have equal integrals over the interval formula_45, using integration by substitution. But on the other hand, since formula_46, the sum of the two integrals is
The Doll that Came Straight from Fairyland The Doll that Came Straight from Fairyland "The Doll That Came Straight From Fairyland" is a short story for children published in 1898 by the suffragist and children's fairytale writer Evelyn Sharp. The first edition was published by John Lane in London, England, in "All The Way To Fairyland" with seven other short stories. Evelyn Sharp was born in 1869 and was the ninth of eleven children. She had three years of schooling in London where she made her living. Evelyn's first publication was an article about fairy tales which led to "Wymps and other Fairy Tales" (1896) and "All