Montour American. (Danville, Pa.) 1866-1920, 1901-01-31
THREE ODD NUMBERS
IRREGULARITIES THAT HEDGE ABOUT
THREE, SEVEN AND NINE.

They Have Been Favorite Numerals
mt All Times All the World Over
and Disclose Some Queer Results
When Twisted About a Bit.
Nobody has ever satisfactorily account
ed for the popular partiality for odd num-
bers. This is the third time" exclaims
Falstaf, ON the occasion of a crisis in his
relations with one of the merry wives
Of Windsor 81 hope good luck lies in
odd numbers; they say there's divinity
in odd numbers, either in nativity,
chance C- death" And it is scarcely
necessary to say that the belief is much
older than Sir John Falstaff. Three,
seven and nine appear to have been the
favorite numbers all the world over. The
ancients had three fates three furies and
three graces; Neptune's trident had three
prongs, Jupiter's thunderbolt three forks,
and Cerberus three heads. We have
three estates of the realm, a man who
accepts bill has three days grace, and
three persons cOngregated together may
make riot. Shakespeare was well aware
that he must have neither more nor less
than three witches in Macbeth" and
that the brindled cat must new thrice,
and our popular folklore insists upon three
merry men, three blind mice and three
wise men of Gotham. Three meals a
day is the usual scale of feeding.
OF a more mystical character than
three is the figure seven, or, at any rate,
it has larger number Of religious appli-
cations. Noah had seven days warning
of the coming Of the food, and when it
came he took fowls by sevens and clean
beasts by sevens into the ark; the ark
touched on Mount Ararat in the seventh
month, and after seven days q dove was
sent out, followed seven days afterward
by another. In Pharaoh's dream there
were seven fat and seven lean kline,
which Joseph interpreted to mean seven
years of plenty and seven years Of fam
inc. At the destruction of Jericho sew
en- priests bore seven trumpets seven
days, and on the seventh day they walked
round the city seven times. after which
the walls fell. In the apocalypse almost
everything is seven, except the number Of
the beasts. There are seven churches. sew
en- golden candlesticks, seven lamps be-
fore seven spirits, the book with seven
seals, the lamb with seven horns and sew
en- eyes, seven angels with seven seals.
seven kings, seven thunders. seven thou
sand slain, the dragon with seven heads
and seven crowns. seven angels bring
seven plaques, and there are seven walls
of wrath
In merely secular matters seven occurs
frequently enough. We have seven Won
ders of the world. seven champions Of
Christendom. seven sleepers. seven wise
H.. cine
seven ages OF man, and our ordinary
leases are made for seven or n multiple
of seven years.
But however mystically significant
three and seven may be. they cannot lay
claim to any such peculiarities as are the
property OF the figure nine. That the
ancients had nine muses.. nine rivers in the
internal regions. hydra with nine heads
and nine gods for Lars Porsena to swear
by, or that in modern times cat has
nine lives. that il takes nine tailors TO
make n man. or that possession is nine
points OF the law. are facts that pale into
insignihcance after one has once sat
down with pencil and paper to investigate
some OF the special peculiarities OF the
figure nine For instance. IL you null
tiply nine by any other number you will
find that the figures composing the prod
uct when added together will always
amount to nine. Thus:
px2a IS and r s=9.
exSs 81 and 100.
ox4 . 80 and + G 80.
and so on to any extent. On arriving at
IL times 0 we find what appears to be an
exception. for the digits OF 90 equal Is.
But it will be observed that IL is a null
tiple of 8 and, moreover that the figures
composing it add up TO 8. Another pc
cularity OF this figure is discovered by
taking any number OF two figures of
which the first figure is of greater value
than the second, reversing these figures
and then subtracting the number thus OBJ
tanned from the original number What
ever figures we may take, the result will
always be 0 or some multiple of 8. The
smallest possible number of two figures
of which the first figure is larger than
the second is q. Reverse the figures,
and we get II. Subtract II from IL and
the remainder is 8. The largest similar
number is 09. Reverse these. and we get
80. Subtract SO from 0S, and again the
remainder is found to be ..
Or let us take a case in which 9 COM
bines with the mystic {. The number 80 is
not divisible by .. But il we add to it.
either in front. when it makes IG5. or in
the middle, when it makes GI5. or at the
end, when it makes G57. we shall find
that every one of these numbers is divis-
ible by 8. 1t is not every number which
can thus be dealt with. and the reader
may find an evenings entertainment in
trying to puzzle out the reason why. An
example of a higher number may be Civ
en- by way of a little assistance: S96.5I3
is not divisible by 9, but if the mystic
7 be added to it, either in front, where il
raises the amount by 100000. or in
any other position. each one Of the eight
various amounts which may thus be oh
tanned becomes divisible by D.
The fact can be verified by any child
who has mastered the first four rules Of
arithmetic, but the explanation Of il is
another matter. To Senior Wranglers or
even to Junior Optimes there may be
nothing very mysterious about all this
And it may be that IL any OF US would
only put himself through q course Of the
higher algebra. digest the integral calru.
lus and master few amusing treat ses
on the theory of differences oil that now
seems so perplexing in the matter would
become as plain as the multiplication Ia
ble.-London Globe.