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# sci.math FAQ: Indiana Bill sets value of Pi to 3

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```Archive-name: sci-math-faq/indianabill
Last-modified: February 20, 1998
Version: 7.5

Indiana bill sets the value of pi to 3

The bill House Bill No. 246, Indiana State Legislature, 1897,
reportedly set the value of pi to an incorrect rational approximation.

The following is the text of the bill:

HOUSE BILL NO. 246

"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 accepted and adopted by the official action of the
legislature of 1897.

"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 circumference, as the area of
an equilateral rectangle is to the square on one side. 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
circles area one and one-fifths times the area of a square whose
perimeter is equal to the circumference of the circle. This is
because one-fifth of the diameter fils to be represented four times
in the circle's circumference. For example: if we multiply the
perimeter 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.

"Section 2. It is impossible to compute the area of a circle on the
diameter as the linear unit without trespassing upon the area
outside the circle to the extent of including one-fifth more area
than is contained within the circle's circumference, because the
square on the diameter produces the side of a square which equals
nine when the arc of ninety degrees equals eight. 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. Furthermore, it has revealed the ratio
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, disclosing the fourth important fact, that the
ratio of the diameter and circumference is as five-fourths to four;
and because of these facts and the further 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.

"Section 3. In further proof of the value of the author's proposed
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 having been already
accepted as contributions to science by the American Mathematical
Monthly, the leading exponent of mathematical thought in this
country. And be it remembered that these noted problems had been
long since given up by scientific bodies as unsolvable mysteries
and above man's ability to comprehend."

Will E. Edington in an article published in the Proceedings of the
Indiana Academy of Science describes the fate of the bill in the
committees of the Indiana legislature. First it was referred to the
House Committee on Canals, which was also referred to as the Committee
on Swamp Lands. Notices of the bill appeared in the Indianapolis
Journal and the Indianapolis Sentinel on Jan. 19, 1897, both of which
described it a a bill telling how to square circles. On the same day,
"Representative M.B.Butler, of Steuben County, chairman of the
Committee on Canals, submitted the following report:

"Your Committee on Canals, to which was referred House Bill No.246,
entitled an act for the introduction of a mathematical truth, etc.,
has had the same under consideration and begs leave to report the
same back to the House with the recommendation that said bill be
referred to the Committee on Education."

The next day, the following article appeared in the Indianapolis
Sentinel:

"To SQUARE THE CIRCLE

"Claims Made That This Old Problem Has Been Solved. "The bill
telling how to square a circle, introduced in the House by
Mr.Record, is not intended to be a hoax. Mr. Record knows nothing
of the bill with the exception that he introduced it by request of
Dr.Edwin Goodwin of Posey County, who is the author of the
demonstration. The latter and State Superintendent of Public
Instruction Geeting believe that it is the long-sought solution of
the problem, and they are seeking to have it adopted by the
legislature. Dr. Goodwin, the author, is a mathematician of note.
He has it copyrighted and his proposition is that if the
legislature will indorse the solution, he will allow the state to
use the demonstration in its textbooks free of charge. The author
is lobbying for the bill."

On "February 2, 1897, ...Representative S.E. Nicholson, of Howard
County, chairman of the Committee on Education, reported to the
House.

"Your Committee on Education, to which was referred House Bill
No.246, entitled a a bill for an act entitled an act introducing a
new mathematical truth, has had same under consideration, and begs
leave to report the same back to the House with the recommendation
that said bill do pass.

"The report was concurred in, and on February 8, 1897, it was
brought up for the second reading, following which it was
considered engrossed. Then 'Mr. Nicholson moved that the
constitutional rule requiring bills to be read on three days be
suspended, that the bill may be read a third time now.' The
constitutional rule was suspended by a vote of 72 to 0 and the bill
was then read a third time. It was passed by a vote of 67 to 0, and
the Clerk of the House was directed to inform the Senate of the
passage of the bill."

The newspapers reported the suspension of the consitutional rules and
the unanimous passage of the bill matter-of-factly, except for one
line in the Indianapolis Journal to the effect that "this is the
strangest bill that has ever passed an Indiana Assembly."

The bill was referred to the Senate on Feb.10, 1897, and was read for
the first time on Feb.11 and referred to the Committee on Temperance.
"On Feb.12 Senator Harry S. New, of Marion County, Chairman of the
Committee on Temperance, made the following report to the Senate:

"Your committee on Temperance, to which was referred House Bill
No.246, introduced by Mr.Record, has had the same under
consideration and begs leave to report the same back to the Senate
with the recommendation that said bill do pass."

The Senate Journal mentions only that the bill was read a second time
on Feb.12, 1897, that there was an unsuccessful attempt to amend the
bill by strike out the enacting clause, and finally it was postponed
indefinitely. That the bill was killed appears to be a matter of dumb
luck rather than the superior education or wisdom of the Senate. It is
true that the bill was widely ridiculed in Indiana and other states,
but what actually brought about the defeat of the bill is recorded by
Prof. C.A. Waldo in an article he wrote for the Proceedings of the
Indiana Academy of Science in 1916. The reason he knows is that he
happened to be at the State Capitol lobbying for the appropriation of
the Indiana Academy of Science, on the day the Housed passed House
Bill 246. When he walked in the found the debate on House Bill 246
already in progress. In his article, he writes (according to
Edington):

"An ex-teacher from the eastern part of the state was saying: 'The
case is perfectly simple. If we pass this bill which establishes a
new and correct value for pi , the author offers to our state
without cost the use of his discovery and its free publication in
our school text books, while everyone else must pay him a
royalty.'"

The roll was then called and the bill passed its third and final
reading in the lower house. A member 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.

"That evening the senators were properly coached and shortly
thereafter as it came to its final reading in the upper house they
threw out with much merriment the epoch making discovery of the Wise
Man from the Pocket."

The bill implies four different values for pi and one for sqrt(2), as
follows: pi' = 16/sqrt(3), 2 sqrt(5 pi/6), 16 sqrt(2)/7, 16/5 ( 9.24 ,
3.236 , 3.232 , 3.2 respectively.) sqrt(2)' = 10/7.

It has been found that a circular area is to the square on a line
equal to the quadrant of the circumference, as the area of an
equilateral rectangle is to the square on one side.

pi' : ((pi'/2))^2 = sqrt(3)/4 : 1 i.e. pi' = 16/sqrt(3) = 9.24.

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 circles area one and one-fifths times the area of a
square whose perimeter is equal to the circumference of the circle.
This is because one-fifth of the diameter fails to be represented
four times in the circle's circumference.

Bit tricky to decipher, but it seems to say ((2 pi'/4))^26/5 = pi i.e.
pi' = 2 sqrt(5 pi/6) = 3.236

Furthermore, it has revealed the ratio of the chord and arc of
ninety degrees, which is as seven to eight,

sqrt(2) : pi/2 = 7 : 8 i.e. pi = 16 sqrt(2)/7 = 3.232

and also the ratio of the diagonal and one side of a square which
is as ten to seven

i.e. sqrt(2) = 10/7 = 1.429

that the ratio of the diameter and circumference is as five-fourths
to four

i.e. pi = 16/5 = 3.2
_________________________________________________________________

--
Alex Lopez-Ortiz                                         alopez-o@unb.ca
http://www.cs.unb.ca/~alopez-o                       Assistant Professor
Faculty of Computer Science                  University of New Brunswick
```