hey this is presh talwalkar reminding
you to mind your decisions
a viral math meme claims that 9 plus 10
is equal to 21.
this is clearly not true in the decimal
base 10 system
but what if the numbers on the left were
in base x and the number on the right
was in base y
could you find values of x and y that
make this equation true
pause the video if you'd like to give it
a try
and when you're ready keep watching to
learn the solution
[Music]
before i get to the answer i want to go
over an important part of mathematical
history so bear with me as i read
wikipedia
the most commonly used system of
numerals is the hindu arabic numeral
system
two indian mathematicians are credited
with developing it aryabhat of kusumpura
developed the place value notation in
the 5th century and a century later
brahmagupta introduced the symbol for
zero
the numeral system and the zero concept
developed by the hindus in india slowly
spread to other surrounding countries
due to their commercial and military
activities with india the arabs adopted
and modified it even today the arabs
called the numerals which they used were
hind or the hindu numeral system
the arabs translated hindu texts a
numerology and spread them to the
western world do their trade links with
them the western world modified them and
called them the arabic numerals as they
learn them from the arabs hence the
current western numeral system is the
modified version of the hindu numeral
system developed in india
so how did the ideas spread to europe
it was in part because of a book
fibonacci wrote liber abbaki in 1202
he called it the modus indorum or the
method of the indians
until this time europe used roman
numerals making modern mathematics
almost impossible
the book thus made an important
contribution to the spread of decimal
numerals
the spread of the hindu arabic system
however as or writes was long drawn out
taking many more centuries to spread
widely and did not become complete until
the later part of the 16th century
accelerating dramatically only in the
1500s with the advent of printing
this is tremendous
fibonacci shared one of the most
important discoveries in mathematics and
yet it took hundreds of years to spread
through europe
i'd like to point this out whenever
people think the base 10 system is just
natural and something we would have
developed from 10 fingers it's not
something so obvious and we should
credit the mathematicians who discovered
it and appreciate its entire history
so now let's solve our problem
each of the numbers on the left is in
base x nine in base x will be equal to
nine
we now convert one zero in base x
this expands to be one x or just x
we now expand two one in base y this
will be 2 y plus 1.
we now simplify this equation
we subtract 1 from both sides and then
we divide by 2 and we further simplify
so we have the equation y is equal to
four plus x over two
but not all values of x and y will work
remember we're dealing with number bases
and standard number bases are positive
integers
furthermore we have x over two in order
that y is an integer we're going to need
x to be a positive even number
there's one more consideration
we have 9 in base x
typically we would use the digit 9 if
our base is at least 10
we wouldn't use it if our base is 9 or
less
so we now consider possible values of x
and y
the smallest value of x could be 10
which would mean y is equal to 9 and
this is a true equation
we now increment by 2
12 and 10 will be another valid solution
we can then increment x by 2 again and
we get another value for y
and we can continue this process
indefinitely as long as we have x and y
is equal to 4 plus x over 2 this will be
a valid solution
so at first glance 9 plus 10 is equal to
21 is just a false equation and there's
no way that you can correct it
but if we think about number bases
they're actually an infinite number of
ways that we can make this equation true
remarkable
thanks for watching and for making mind
your decisions one of the best channels
on youtube
thanks for watching and thanks for your
support
[Music]
you