How many angels can dance on the head of a pin? dancing on a needle's point occurs in an expository work by the English divine, William Sclater (1575-1626). In "An exposition with notes vpon the first Epistle to the Thessalonians" (1619), Sclater claimed that scholastic philosophers occupied themselves with such pointless questions as whether angels "did occupie a place; and so, whether many might be in one place at one time; and how many might sit on a Needles point; and six hundred such like needlesse points." Harrison proposes that the reason an English writer first introduced the "needle’s point" into a critique of medieval angelology is that it makes for
Koch snowflake snowflake. After each iteration, the number of sides of the Koch snowflake increases by a factor of 4, so the number of sides after iterations is given by: If the original equilateral triangle has sides of length , the length of each side of the snowflake after iterations is: the perimeter of the snowflake after iterations is: The Koch curve has an infinite length because the total length of the curve increases by a factor of four thirds with each iteration. Each iteration creates four times as many line segments as in the previous iteration, with the length of each