**das@ecsvax.UUCP** (04/05/84)

Ref dciem.814,815,816 and brl-vgr.3076 -- see first ref for other references. It's difficult to know what "the value of pi" means when the given information contradicts itself. The first part of the Indiana bill certainly implies pi=4, even though Mark Brader gives a convincing case that the author thought 3.2 was the right value. If the area of a circle is (pi*r/2)^2 (as in the bill) and is also pi*r^2 (as we all know it to be), it follows that pi has to be 4. The argument for 3.2 is similar to this, but it is based on a later part of the bill. The correct author's name for The History of Pi is Petr Beckmann. Complete reference and more details on related subjects may be found in my book Interface: Calculus and the Computer, Saunders College Publishing, 1984 (second edition). David A. Smith Department of Mathematics Duke University Durham, NC 27706 (919) 684-2321 {decvax,akgua}!mcnc!ecsvax!das

**ntt@dciem.UUCP (Mark Brader)** (04/09/84)

I'm afraid I must challenge escvax!das (David Smith)'s interpretation. It's difficult to know what "the value of pi" means when the given information contradicts itself. The first part of the Indiana bill certainly implies pi=4, even though Mark Brader gives a convincing case that the author thought 3.2 was the right value. If the area of a circle is (pi*r/2)^2 (as in the bill) and is also pi*r^2 (as we all know it to be), it follows that pi has to be 4. The argument for 3.2 is similar to this, but it is based on a later part of the bill. First, you can't use A = pi*r^2, because the author says explicitly that "the present rule in computing the circle's area is entirely wrong", and should be what amounts to A = (pi*r/2)^2 INSTEAD OF A = pi*r^2. The bill certainly does contradict itself elsewhere, but not on this point. Pi is defined as the ratio of the circumference and diameter, *not* as the ratio of area and the square of the radius, even though in the real world they are the same... at least, that's what it says in any book I've ever seen. The "later part of the bill" gives the reciprocal of this explicitly as (5/4)/4, which equals 1/3.2, which should settle it. Besides, the author claims that areas under the "rule in present use" are too large; if he intended the formula to be A = 4*r^2, then they he would say they were too small. Substituting pi=3.2 in A = (pi*r/2)^2 gives A = 2.56*r^2, and the real areas *are* larger than this. (You may as well suggest that this formula means that pi=2.56.) The bill really does make pi equal to 3.2. However, the quoted item makes it clear why some people seem to have thought it was 4, which I didn't understand. It's been some years (and miles) since I read Beckmann's "A History of Pi"; I think Beckmann just said the bill was contradictory; anyone want to say what he did say about the contents? I think any followups to this should be in net.math only. Mark Brader