ntt@dciem.UUCP (Mark Brader) (03/30/84)
I posted to net.misc as well because that's where the topic originated. The article posted there by Betsy Hanes Perry (dartvax!betsy) is correct in substance (in particular, there was no religious connection, just a crank). I have more facts and some corrections. I am reasonably sure that any references to *any* state setting pi to 3 (or any other value) by legislation really refer to this event. The law was proposed in Indiana in 1897. It would have set the value of Pi to 3.2 (*not* 3); also, sqrt(2) would become 10/7, and the area of a circle would become ((pi^2)/4)*r^2 -- which is 2.56*r^2 since pi = 3.2. The bill was passed by the state House of Representatives, but the state Senate "suspended consideration indefinitely", so it never became law. Two longer following articles will contain more story (and source info), and the complete text of the bill with my annotations. Both may be amusing. Mark Brader
ntt@dciem.UUCP (Mark Brader) (03/30/84)
See part 1 article for netnews References:; the References: line grew
too long for our system to handle.
My source for the information following, and for the text of the bill in
the part 3 article, is a 5-page article that appeared in the 1930's in
the Proceedings of the Indiana Academy of Science. That article is
researched from primary sources: it gives specific citations in the
Indianapolis newspapers and the House and Senate Journals from 1897,
and a PIAS article written from memory in 1916. I have only a many-
generationed photocopy of the 1930's article, kindly sent to me by
Russ Archer of mhuxr. There is no direct indication of the date,
but July 1935 is referred to as "the past summer" in the article.
In case anyone wants to trace it, the author is Will E. Edington, the
title is "House Bill No. 246, Indiana State Legislature, 1897", and
the page number in the PIAS is 206.
I was unable to find any reference by Martin Gardner to the story,
neither in "Fads and Fallacies in the Name of Science" as suggested
by John Hobson (ihuxq!amigo2) nor in his Scientific American columns.
He did write a column about pi in June(?) 1960. I have seen brief
references in several places, including the Guinness Book of World
Records. Frequently these references give the wrong wrong value of Pi.
It was 3.2, not 3 as the Bible seems to suggest, nor 4 as Guinness says.
So, what happened?
The author of the bill was Dr. Edwin J. Goodwin, an M.D., of
Solitude, Indiana. As Betsy Perry said, he was a crank mathematician.
Presumably wanting recognition for his supposed discovery,
he contacted his Representative, one Taylor I. Record, with his
epoch-making suggestion: if the State would pass an Act recognizing
his discovery, he would allow all Indiana textbooks to use it without
paying him a royalty. (Dr. Goodwin seems to have had a distorted
idea of the powers of copyright, as well.)
Nobody in the Indiana Legislature knew enough mathematics to know that
the "discovery" was nonsense. The bill was introduced in the House
of Representatives on Monday, January 18, 1897, and (of course :-) ) it
was referred to the Committee on Canals, often called Swamp Lands.
The next day they reported back with the recommendation that it be
referred to the Committee on Education. The day after that, the
State Superintendent of Public Education was reported in a newspaper
article to be supporting the bill.
Well, the Committee on Education approved the bill! It was introduced
for second reading on Friday, February 5, and passed 72-0. Then "Mr.
Nicholson moved that the constitutional rule requiring bills to be
read on three [different] days be suspended", and it was, and the
bill had its third reading, and passed 67-0.
At this point the text of the bill was published "and, of course,
became the target for ridicule", "in this and other states".
One of the papers said, "This is the strangest bill that has ever
passed an Indiana Assembly".
By this time a real mathematician, Prof. C. A. Waldo, had learned
what was going on. In fact, he was present when the bill was read
on February 5. ("...imagine [the author's] surprise when
he discovered that he was in the midst of a debate upon a piece of
mathematical legislation. An ex-teacher was saying ... 'The case is
perfectly simple. If we pass this bill which establishes a new and
correct value for Pi, the author offers ... its free publication in
our school text books, while everyone else must pay him a royalty'",
Waldo wrote in the 1916 article.) But the House had passed the bill.
Fortunately, Indiana has, or had, a bicameral legislature. The bill
came up for first reading in the Senate on Thursday, February 11.
Apparently deciding to have some fun, they referred it to the Committee
on Temperance. The Committee reported back on Friday, February 12,
approving the bill, which then had its second reading.
The Indianapolis Journal reported what happened: "The Senators
made bad puns about it, ridiculed it, and laughed over it. The fun
lasted half an hour. Senator Hubbell said that it was not meet for
the Senate, which was costing the State $250 a day [!], to waste its
time in such frivolity ... He moved the indefinite postponement of
the bill, and the motion carried. ... All of the senators who
spoke on the bill admitted that they were ignorant of the merits of
the proposition. [In the end,] it was simply regarded as not being a
subject for legislation."
Mark Braderntt@dciem.UUCP (Mark Brader) (03/30/84)
See part 1 article for netnews References:.
/* Following is the text of Indiana House Bill #246 of 1897, with my own anno-
tations (in comment signs and exdented, like this text). In my annotations, A,
r, d, c, and s are respectively the circle's area, radius, diameter, circumfer-
ence, and side of the inscribed square. */
A bill for an act introducing a new mathematical
truth and offered as a contribution to education to be
used only by the State of Indiana free of cost by paying
any royalties whatever on the same, provided it is ac-
cepted and adopted by the official action of the leg-
islature of 1897.
/* You normally have to pay royalties on mathematical truths? The Pythagoras
estate must be doing well by now... */
SECTION 1.
Be it enacted by the General Assembly of the State
of Indiana: It has been found that a circular area is to
the square on a line equal to the quadrant of the cir-
cumference, as the area of an equilateral rectangle is
to the square on one side.
/* The part after the last comma is a remarkable way of saying "as 1 is to 1".
In other words, this says A = (c/4)^2, which is the same as A = (pi*r/2)^2 =
(pi^2/4)*r^2 instead of the actual pi*r^2. */
The diameter employed as the linear
unit according to the present rule in computing the
circle's area is entirely wrong, as it represents the
circle's area one and one-fifth times the area of a
square whose perimeter is equal to the circumference of
the circle.
/* The formula A = pi*r^2 is interpreted as A = d*(c/4), which is correct.
The author claims that the d factor should be c/4, so the area by the author's
formula is to the area by the real formula as c/(4*d) = pi/4. Since he be-
lieves pi = 3.2, this ratio is 3.2/4 = 4/5. Therefore the area by the author's
rule is 1/5 smaller than the actual area. He apparently thinks this means the
other area is 1/5 larger than his area, which of course would actually require
the ratio to be 5/6. */
This is because one-fifth of the di-
ameter fails to be represented four times in the
circle's circumference.
/* In other words, c = (1-1/5) * (4*d); consistent with pi = 3.2. */
For example: if we multiply the per-
imeter of a square by one-fourth of any line one-fifth
greater than one side, we can in like manner make the
square's area to appear one fifth greater than the fact,
as is done by taking the diameter for the linear unit
instead of the quadrant of the circle's circumference.
/* He says that if we consider the area of a square of side x to be
(4*x)*(x/4) and we replace the second x by (1+1/5)*x, we get an area 1/5 too
large, and this is analogous to using d in place of c/4 with the circle. */
SECTION 2.
It is impossible to compute the area of a circle
on the diameter as the linear unit without tresspassing
upon the area outside the circle to the extent of in-
cluding one-fifth more area than is contained within the
circle's circumference, because the square on the diame-
ter produces the side of a square which equals nine when
the arc of ninety degrees equals eight.
/* I can only assume that "nine" is a mistake for "ten". */
By taking the quadrant of the
circle's circumference for the linear unit, we fulfill
the requirements of both quadrature and rectification of
the circle's circumference.
/* Getting repetitive here... */
Furthermore, it has revealed the ra-
tio of the chord and arc of ninety degrees, which is as
seven to eight, and also the ratio of the diagonal and
one side of a square which is as ten to seven, disclos-
ing the fourth important fact, that the ratio of the di-
ameter and circumference is as five-fourths to four; and
because of these facts and the futher fact that the rule
in present use fails to work both ways mathematically,
it should be discarded as wholly wanting and misleading
in its practical applications.
/* The meat of the bill. He says that s/(c/4) = 7/8, and d/s = 10/7, there-
fore d/c = (10/7)*(7/8)/4, which he reduces only as far as (5/4)/4. Of course
this is 5/16, and gives pi = c/d = 16/5 = 3.2. It also implies that the square
root of 2 is 10/7. */
SECTION 3.
In further proof of the value of the author's pro-
posed contribution to education, and offered as a gift
to the State of Indiana, is the fact of his solutions of
the trisection of the angle, duplication of the cube and
quadrature of the circle having been already accepted as
contributions to science by the American Mathematical
Monthly, the leading exponent of mathematical thought in
this country.
/* Not bad, eh? Of course these are problems well known to have no solution
within the usual constraints (compass and straightedge construction only), and
the third one is essentially equivalent to the matter of the bill. I guess the
A.M.M. had a policy of politely acknowledging crankish submissions, and the au-
thor took that as acceptance. Ah well, I suppose that if this bill was enact-
ed, then it would become true that the A.M.M. had accepted the solutions. */
And be it remembered that these not-
ed problems had been long since given up by scientific
bodies as unsolvable mysteries and above man's ability
to comprehend.
/* "Given up" is not the same as "proved insoluble"!
Posted by Mark Brader; see part 2 article for source.
Spelling is reproduced as in the source (I hope). */gwyn@brl-vgr.ARPA (Doug Gwyn ) (03/31/84)
If anyone is interested in this, I recommend that he read a book by Petr Bergmann (I got the first name right but may have flubbed the last) entitled something like "A History of Pi". It has among other things some more information on attempts to legislate its value.