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sci.math FAQ: Bill sets Pi = 3


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Archive-Name: sci-math-faq/specialnumbers/lawPieq3
Last-modified: December 8, 1994
Version: 6.2



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 tresspassing 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 consitutional 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 fils 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


     _________________________________________________________________



    alopez-o@barrow.uwaterloo.ca
    Tue Apr 04 17:26:57 EDT 1995

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