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A
Straight Dope Classic from Cecil's storehouse of human knowledge22-Feb-1991
Dear Cecil:
In Science magazine a while back an article about the latest
attempts to calculate pi to the umpteen zillionth decimal place
made a passing reference to a curious Oklahoma law. It said
Oklahoma legislators had passed a law making pi equal to 3.0. I
also remember Robert Heinlein in one of his novels mentioning that
Tennessee had passed a similar law. Did either of these states ever
pass such a law? Are they still on the books? What are the
penalties if I proclaim that pi equals 3.14159...? --Wulf Losee,
Andover, Connecticut
Dear Wulf:
Cecil had heard this story too, only the state in question was
Kansas, leading him to believe the whole thing was made up by
big-city sharpies having a little fun at the expense of the
rustics. However, with the help of Joseph Madachy, editor of the
Journal of Recreational Mathematics, I've learned the story does
have a germ of truth to it.
It happened in Indiana. Although the attempt to legislate pi was
ultimately unsuccessful, it did come pretty close. In 1897
Representative T.I. Record of Posen county introduced House Bill
#246 in the Indiana House of Representatives. The bill, based on
the work of a physician and amateur mathematician named Edward J.
Goodwin (Edwin in some accounts), suggests not one but three
numbers for pi, among them 3.2, as we shall see. The punishment for
unbelievers I have not been able to learn, but I place no credence
in the rumor that you had to spend the rest of your natural life in
Indiana.
Just as people today have a hard time accepting the idea that the
speed of light is the speed limit of the universe, Goodwin and
Record apparently couldn't handle the fact that pi was not a
rational number. "Since the rule in present use [presumably pi
equals 3.14159...] fails to work ..., it should be discarded as
wholly wanting and misleading in the practical applications," the
bill declared. Instead, mathematically inclined Hoosiers could take
their pick among the following formulae:
(1) The ratio of the diameter of a circle to its circumference is
5/4 to 4. In other words, pi equals 16/5 or 3.2
(2) The area of a circle equals the area of a square whose side is
1/4 the circumference of the circle. Working this out
algebraically, we see that pi must be equal to 4.
(3) The ratio of the length of a 90 degree arc to the length of a
segment connecting the arc's two endpoints is 8 to 7. This gives us
pi equal to the square root of 2 x 16/7, or about 3.23.
There may have been other values for pi as well; the bill was so
confusingly written that it's impossible to tell exactly what
Goodwin was getting at. Mathematician David Singmaster says he
found six different values in the bill, plus three more in
Goodwin's other writings and comments, for a total of nine.
Lord knows how all this was supposedly to clarify pi or anything
else, but as we shall see, they do things a little differently in
Indiana. Bill #246 was initially sent to the Committee on Swamp
Lands. The committee deliberated gravely on the question, decided
it was not the appropriate body to consider such a measure and
turned it over to the Committee on Education. The latter committee
gave the bill a "pass" recommendation and sent it on to the full
House, which approved it unanimously, 67 to 0.
In the state Senate, the bill was referred to the Committee on
Temperance. (One begins to suspect it was silly season in the
Indiana legislature at the time.) It passed first reading, but
that's as far as it got. According to The Penguin Dictionary of
Curious and Interesting Numbers, the bill "was held up before a
second reading due to the intervention of C.A. Waldo, a professor
of mathematics [at Purdue] who happened to be passing through."
Waldo, describing the experience later, wrote, "A member [of the
legislature] then showed the writer [i.e., Waldo] a copy of the
bill just passed and asked him if he would like an introduction to
the learned doctor, its author. He declined the courtesy with
thanks, remarking that he was acquainted with as many crazy people
as he cared to know."
The bill was postponed indefinitely and died a quiet death.
According to a local newspaper, however, "Although the bill was not
acted on favorably no one who spoke against it intimated that there
was anything wrong with the theories it advances. All of the
Senators who spoke on the bill admitted that they were ignorant of
the merits of the proposition. It was simply regarded as not being
a subject for legislation."
As for Representative T.I. Record--well, I haven't been able to
confirm this. But some say he changed his name to Quayle.
THE WISDOM OF SOLOMON:
NOT WHAT IT'S CRACKED UP TO BE
Dear Cecil:
Your response to the question about attempts to legislate pi
suggests not only that your scholarship is weak but that you are a
heathen. When King Solomon constructed the Temple of Jerusalem, the
Second Book of Chronicles, chapter 4, verses 2 and 5, tells us:
"Then he made the Sea [a big tub] of cast bronze, ten cubits from
one brim to the other; it was completely round. Its height was five
cubits and a line of thirty cubits measured its circumference. It
was a handbreadth thick; and its brim was shaped like the brim of
a cup..... It contained three thousand baths."
The ratio of 30 cubits for the circumference to 10 cubits for the
diameter "from one brim to the other" of the "completely round"
circle gives the value of pi as being exactly 3. Perhaps reliance
on the Word of God motivated the Indiana legislators you trashed.
You should have checked with the ultimate reference. --H.K.S.,
Springfield, Virginia
Cecil replies:
Some of the mail I get is unbelievable. As I attempted to point
out, the Indiana legislature did not consider making pi equal to 3,
but rather to 3.2, 4, or approximately 3.23, depending on which
formula you used. Neither the text of the bill nor any of the
commentaries regarding it refer to the Bible. Perhaps Tennessee,
Oklahoma, Kansas or one of the other states I mentioned was the one
that attempted to a legislate a pi of biblical proportions.
Interesting you should bring this up, though. In 150 A.D. a Hebrew
rabbi and scholar named Nehemiah attempted to explain away the
anomaly in Chronicles by saying that the diameter of the tub was 10
cubits from outer rim to outer rim, whereas the 30 cubit
circumference was measured around the inner rim. In other words,
the difference between the biblical notion of pi and the actual
value may be accounted for by the width of the tub's walls. How's
that for tap dancing, eh? Nehemiah lived a long time ago, but I
feel he's my spiritual kin.
--CECIL ADAMS
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