Savannah morning news. [volume] (Savannah) 1868-1887, 1884-04-20
AN ALGEBRAIC GENIUS.
A Butcher Solves Problems Which Pose
College Professors.

PhitfdeLDhfd EnQUfPer.
Ardmore. on the line of the PennsvIya-
MIA Railroad just outside Of the city, has
a butcher, whose father was a butcher be-
fore him, and whose four brothers are
butchers, not to say that there is anything
remarkable in that. This butcher indivi-
dualiZes his existence by the inherited
name of Duncan. and with the name of
Duncan all that is strange, old, and mys-
ii cal is intimately associated with the
hearts and minds Of all the good people of
ArdmOre. And the reason Of this is Obvi-
Gus. His fame was disclosed first through
the impetuOsity of some college youths,
whose admiration for him can be explain
ed upon a basis more practical than hon
est.
A great problem was given out in the
University of Pennsylvania, some time
ago. and the ArdmOre butcher enjoys the
distinction of being the only person who
holds the key to its solution. The prob
lem is this: Take room 40 feet long and
IS feet wide, what is the longest piece of
carpet, yard wide, that can be laid on it
without cutting?
To find the hypothenuse Of the rectan-
gle formed by the given dimensions Of the
room is a very simple process in mensura-
ton, but to find the exact length of a roll
of carpet that VIII iii in it without cut
ting of the square corners is what has
disturbed the tranquility Of a college
professor. The example as really a puZ-
zle, in which a person is liable to over
look one or more OF its hidden factors in
the attempt to reach a correct solution.
1t is therefore impossible to demonstrate
it clearly by any known rules Of algebra.
The problem when given out at the uni
versity was shown to Samuel Duncan, the
ArdmOre butcher mentioned above, by
student named Gross and in QVGGflV forty
minutes Mr.. Duncan reached, by theO-
retical solution on paper, a result that
can be proved by actual measurement to
be accurate. The answer is 1906. How
to obtain the decimal fraction is the sub
tie point in the problem, and it is said
that it cannot be reached by algebraic
rules.
And this is Just where Mr.. Duncan
steps upon the scene with a record more
than usually brilliant as a natural born
mathematician. He has been known by
reputation to the teachers of adjacent
parts of Montgomery county, as well as to
the students at some of the excellent col
leges in that vicinity, for several years as
a person capable Of succeeding in almost
any task in mathematics. On several re-
cent occasions he has astOnished people
by prOpOunding difficult questions in
arithmetic and finding the correct an
swers in less time than the most expert
calculatOrs are capable of. 1t has been
the custom of college pupils to bring eX-
amples to him when they were unable to
solve them, and his popularity among
students is commensurate with the amount
of assistance which he is always willing
to give them.
After Mr.. Duncan had found the result
Of the problem about the strip of carpet,
several persons applied to him to be shown
the work bV which hp reached the answer
The calculation is spread over three pages
OF fOolscap paper, and for these pieces OF
paper Mr.. Duncan has been offered by a
college student, near ArdmOre, $40. But
the offer was refused because some stu
dents Of the university have agreed to pay
him $25 for the demonstration.
The remarkable talent Of the ArdmOrc
butcher is associated with some curious
freaks. He can perform one which an or
binary man would attribute to the
mysteries of second sight or some other
( hidden power. This is nothing less than
to sit down and do an example on a sheet
/ of paper with his right hand, while he per.
! forms simultaneously different example
! ON another sheet of paper with his left
/ hand, reaching the correct answers OF
both Of them in less time than il would
/ take another person to do either one OF
/ them separately. Another talent he has
is to multiply backward. The mathemati
/ cal genius can write a row of figures re-
versed and multiply them by three or fOul
| integers, reaching the answer will
! lightning-like rapidity. The work can be
| proved by holding the paper up to the
/ light and Transforming the figures to theil
normal position
The Ardmore butcher is 80 years old
His four brothers know no more abou
I figures than is common with most men
He left school at the age of Is. having
/ progressed, up to that time, as far as bi
I quadratic equations in Green's algebra
1 When he first took up the study Of algebr;
he performed his work so readily that hi,
! teacher, Mr.. Haas, requested him to re
up and demonstrate on the blackboard al
example which he had solved correctly
/ He was unable to explain it because ht
was not acquainted with the rules Of alge
/ bra, and he paid the penalty for his pre-
I cOcity by staying in after school OStensi
/ bly, for disObcdience.
He has whole trunk full Of papers
/ containing the work of examples done by
/ him for several years, and many Of then
have been incorporated in StOddard anC
! Hemphil's textbook on algebra. One O
these examples gives the height of pol,
sixty feet; at the top it is seven inches il
diameter and at the base ten inches; giveI
that 720 coils Of rope are wound arOunC
/ the pole, how far viii q man walk in uu
winding it. The result can be found D.
the rule Of indeterminate series, but i
requires an immense amount of labor, anC
is liable to errors. The solution, as per
formed by the Ardmore mathematician
! covers forty sheets Of paper The answe
\ is 800 miles