The sun. [volume] (New York [N.Y.]) 1833-1916, 1897-02-28
INDIANESSQUAREDCIRCL
Ar dBorTTHE METHOD FORMALLY
IPPROJED IN THE LEGISLATCRE.
it Substitutes the Ratio ga for the Tire
Honored I.iiis-But Prudent People Will
Be Likely TO stick to the Old fIgures-

shA'hy " ShNe ~ ~ "e NssHN-r
From the Indianapolis Journal
Official recognition by one branch Of the Indi-
ana Legislature has been given Dr. Edward
Johnston Goodwin for solving three geometri-
cal problems which have puzzled the brains Of
mathematician since the erection OF the pyra-
mids OF Egypt, AMI which the French Academy
OF Science, in 1875. ami the Royal Society OF
Great Britain in 1915. both declared impossible
OF solution. The first and most important Of
these problems is what has been popularity
termed for centuries the squarinR OF the circle,
or In science the luadraturc OF the circle. The
other two problems solved by DIR. Goodwin are
known In mathematics As trisection Of the anglo
and the duplication OF the cube.
The solution Of these problems Is a matter Of
little interest to the average citizen. but to SCI
cncc the worth OF these solutions cannot DO esti-
mated in money. To the development OF astro-
nomical science their value Is incalculahlc. Tho
mystery surrounding the supposed impossible
ity OF tetsc problems has ever inspired both
crnnks and mathematicians to unceasing
toll in their search for the correct for
mulas. Squaring the circle has been a chimera
~ vague as perpetual motion. and 1t was be-
cause OF the worry and waste OF time In
examining the many alleged solutions pre-
scnted By would.be discovorcrs OF the key to
squaring the circle that the French and English
49, JN"i 49,
the problem was impossible, and refused to
consider the subject further. This action was
decimal 3. l4lG plus tPD. multiplied by the diam
eter OF q circle, would give the circumference
the correct multiple. but Il was taken 50 near
u accura' @ that IL would serve for all purposes,
nna The mathem.ticians Leg II go at that:
Ing the circle eight years ago, bur not until tho
Worlds Fair did he lnaSs any effort 70 get his
the Liberal Arts building tor hanging his charts
and intended TO be present and make hts demon
hibit. but seiim ii. Peabody, chief OF the depart.
m psrn, ai nss E]rgE r 7 the tho s sPs,Sor re 10 nre.e s,s
SIS solution TO. the msthsmaiical Journals.
Dr.; Goodwin then sent his solution 70 the
authority in this country, and the editor Instant
~ accepted It and printed II in the September
number OF l-93, while the Worlds Fair was in
maticians the world over, the scientific journals
at Paris at once communicating with the author
DR.. Goodwin has his formulas and laws derived
from them copyrighted 4 in the United states and
In seven Countries OF Europe.EnsIand. Ger;
spain. During his visit TO Washington he won
the support o. the professors at The National Az
which is tho celebrated Professor Hall.
whose fame /. secure with the discovery
s~tration was accepted by all at the observatory.
The venerable author has q deskful Of letters
America, and, better than ali, a letter from his
agent in London showing that his demonstratio1
was presented to both Huxley and Typdall and
Endorsed by them before II was copyrighted.
The man who has thus shown the errors in the
text books from Euclid's time to LOOMS is a
PetersbHrs. Dec. 30. isas.' 4 wealthy aunt SEM
him TO school and furnished the funds for n
course at the Philadelphia Medical College. For
the vicinity OF Solitude. Posey county, Indiana,
t IN 1h se Ss@gr rsrsi Up pa Ho OF sss 5 ,oMe. fsisrff Hs 10 e
a most modest citizen. refusing all modern
methods % advertising himself. He Is six feet
massive, angular head correctly suggests his
rugged mathematical brain.
The laws for the quadrature OF the circle dis
covered by DIR. Goodwin, which are copyrishted,
ami which he permits tho use. OF for the first
I'M mo IN qa aa 4 afS iRS Sirci sr IS to to i snd the side of a
square whose pcrimeter equals that of the given
circle; rcctihcat!on OF The circle requires 70 iird
q right line equal 10 the circumference OF the
given circle, The square on the line equal to the
arc OF 30 degrees fulnlls both OF the said re
III Is, imposslbl, to quaarate the circle by
taking the diameter AS the linear anti. because
by the quadrant OF the circumference produces
the side OF a square. which equals 8 when tho
Consistent that it should take the side Of i
square whose perirneter equals that OF a greater
ijI,,. 10 m9 is tie sp yvs- so fb; 4 ,r,S wi \, Wo rhs
require a piece OF tire iron eighteen feet 70 bind
a wagon wheel sixteen feet in circumference.
brought to life the ratio OF the chord and arc Of
30 degrees, which Is as 10. and also the ratio OF
the diagonal and one sido OF a square, which 1:
as 1867. These two ratios show the numerical
relation OF iameter TO circumference 10 be as
lt;+
finite ratio t4:t represents no area OF the
circle 70 he more than The orthodox ratio, yet the
ratio 3.l+l6l represents the area OF q circle
whose circumference equ ia 1 plus . per cent.
greater than the Unite ratio lA:i. as will be seen
by comparing the terms OF their respective pro-
portions stated as follows: 1890 !: L.25:+-
:3lilb l.2'32:i
extremes Is equal TO the product Of the means in
the first statement, while they fail 10. agree In
the second proportion. Furthermore, the qlare
on n line equal 10 the arc OF 30 degrees shows
very clearly that the ratio of the circle Is the
same In principle as that OF the square. For eI-
the sum Of its Sides 6Sy one.foaTth Ok one side.
The product equals the sum OF two sides, by ono
side. Again. the number required to express the
units OF length in one-fourth OF u right line Is the
square root o. the number TePrssen;ins The
These properties q the ratio OF tho squars
further sustained by the following formula to
express Tho numerical measure OF. both circles
and square: Let L represent the circumference
OF a circle whose quadrant is unity. Qia the
quadrant, and coz will apply as the numerical
measure OF a circle and n square.
showing that the diameter Is tho. wrong factor
to employ as the line on which 70 meas
on the diameter Is the mean propor-
tional between the circles circumference
and the square clrcumscribing. 1t. The
square Of the quadrant OF the circun-
ference Is the moan proportional between the
circles inscribed square and tho square on tho
diameter as the linear unit. Therefore. tho
product VI the diameter BY one side OF the in
srrihcd square produces a line that is greater
than the circles circumference. That Is to say,
hy taking the diameter as the linear unit In COM
putting the area o. the square, we can make It's
area about ~ per cent. greater than tho fact.
This is because there is about - per cent. OF tho
diagonal not represented four times In tho
s%iIlge'- pcriInrt.r. Another reason that the
diameter should be dis'aricl ~ tho wrong fac
tor 20 etuDlOy ns the linear uu.t l. because IL falls
20 work both ways; and, therefore, Is not mathe-
lnttlcaily trustworthy.
For Instance. the 'ircle whose circumference
equals 81. tho diameter Il lO.lsJB plus, accord
ing TO the ratio l:3.lIlo plus, and tho area IS
sliNiS plus. The square root OF sl.dsis plus
+ o.o-Hi Mus. Now, lot rs multiply the diane
ter lOl-Jb plus 1y thu square roo; 20 see Il tho
product equals sl,tsis plus, which Il should do
the diameter "a tho proper linral unit; 10, 1885
by n.O3B5 plus equals 81 1892 plI-. L. will be
found by extracting the square root OF ~ 1892
plus aud multiplying the diameter, lo.ls55
Mus. by IL and FpuFaflug the gFna EHsIuTB often