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
Five points determine a conic the answer is given in terms of the multiset coefficient, more familiarly the binomial coefficient, or more elegantly the rising factorial, as: This is via the analogous analysis of the Veronese map: "k" points in general position impose "k" independent linear conditions on a variety (because the Veronese map is biregular), and the number of monomials of degree "d" in formula_18 variables ("n"-dimensional projective space has formula_18 homogeneous coordinates) is formula_20 from which 1 is subtracted because of projectivization: multiplying a polynomial by a constant does not change its zeros. In the above formula, the number of points "k" is