Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang

III. Methods and tools
writrs of The Simpsons tlvision
Th
somtims ommuniat with thir
sris
viwrs y asually
mathmatially-inlind
nar misss into th akground
dropping
mathmatis is mor than a uriosity or
Nar-miss
for pratial joks. Th rason pianos hav
asis
kys in an otav, for xampl, is du to a nar
12
Th two most important musial intrvals
miss.
an otav (a frquny ratio of 2:1) and a fifth (a
ar
of 3:2), ut it is impossil to divid an otav
ratio
a way that nsurs all th fifths will prft.
in
is mathmatially impossil to ronil th
It
frqunis (tons) of otavs and fifths.
diffrnt
you an gt vry los y dividing th otav
“But
12 qual half-stps, svn of whih giv you
into
frquny ratio of 1.498. That’s good nough for
a
also th Ramanujan onstant: e π √163 ,
Considr
almost quals a whol numr:
whih
sns. In th pisod “Th Wizard of
of
Trra”, Homr Simpson writs
Evrgrn
th quation on thir alulators may
hkd
n shokd to find that Homr Simpson
hav
disprovd Frmat’s last thorm! In fat,
had
alulators ar not pris nough to
most
is a vry nar-miss. Frmat’s last
whih
is saf.
thorm
writrs of The Simpsons ar known for
Th
rfrns to advand mathmatis
inluding
th show. Simon Singh, author of Fermat’s
in
(1998) and The Simpsons and Their
Enigma
Secrets (2013), xplains furthr in
Mathematical
linkd vido.
th
trms: Homr’s last
Sarh
YouTu
thorm
How
262,537,412,640,768,743.99999999999925.
thr irrational numrs omin to form a
do
numr? Could it a lu to a dpr
rational
of mathmatis? Th mathmatiian John
pi
misss hav inspird pratial appliations
Nar
wll as uriosity in mathmatiians to look
as
and dig dpr. Thy an srv as lus
losr
what disovris might tru, y
aout
almost tru. Mathmatiians disovr
ing
misss through xprimntation, play,
nar
imprftions, and trial and rror—
ral-world
that ar not typially assoiatd with
words
11
Box 11.4: D’oh! That time Homer Simpson nearly solved Fermat’s last theorem
out th quation
3987 12 + 4365 12 = 4472 12
violats th thorm that a n + b n = c n
whih
no intgr solution if n > 2. Viwrs who
has
show th lft sid of th quation:
3,987 12 + 4,365 12 = 4,472.0000000070576171875 12
Baz, among othrs, thinks so.
most popl” (Lam 2017).
mathmatialmthods.
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