# Hypotheical Math

You have a cake. 20cm in height, and 15cm in radius. Say you slice it in half, and half again, and again and again until you reach the moon from sea level.

Show your work for how many slices it would take.

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I'll reach the moon by slicing a pie
Elaborate

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Purely intellectual question

Why would you reach the moon? You didn't mention stacking them.

yes, stacking...

I will assume that what you are ACTUALLY asking is how many slices it would take if you start with 1 cake, stack 1/2 on top of it, then 1/4... 1/2^n. Let's begin by setting this as a summation series with the following form:
$\sum_{i=0}^{n}{\dfrac{1}{2^{n}}$
The infinite limit of this sum is 2, and since the moon is not 40cm away, you could never reach the moon no matter how many slices you add.

$\sum_{i=0}^{n} {\dfrac{1}{2^{n}}$

incorrect, assume that the cake can be sliced infinitely

What? You reach 40 cm after one slice. You're cutting half the cake and stacking it on the other half. 20 + 20 = 40.
You still have 7.5 cm of cake to halve infinitely, and the cake's height will double everytime

you don't

Dude, the thickest layer is in the bottom. You slice the cake in half, then cut the half in half, then that half in half, then the half of half of half in half etc.

can i stack them if i slice the cake on its side? one slice will get me 60cm so i can use fewer slices. nom

363,104 km from earth to moon at closest point
=36,310,400,,000 cm
/20=1,815,520,000
-20=1,815,519,980

1,815,519,980 slices.

incorrect

In that case, the height increases by 20 cm everytime infinitely, since the width will never be 0. Then it's literally
(distance from moon to earth in cm)
divided by 20.

prove that it is incorrect

It's 1/20 * log base 2 of the distance from the earth to the moon because the height of the cake doubles each time.

Wrong, are you gonna slice the atoms in half?

see

Euclid would know the answer. Only clue I will give

1 + 2= 3
1 + 2 + 4 = 7
1 + 2 + 4 + 8 = 15

20 + 40 = 3(20)
20 + 40 + 80 = 7(20)
20 + 40 + 80 = 15(20)

Teehee

F-

1 + 2 + 4...n-3 terms... = 1,815,519,980

I can't go past this, I'm still in middle school

incorrect

29?

33?

it was all just a pie in the sky anyways

watches numberphile once

Engineer here, even if you could slice the cake thin enough (which you can't) it would be impossible to reach the moon using the cake.

OP's question was very stupidly worded. When he says the cake is sliced in half and added on top, he ACTUALLY means the entire current stack is sliced then added on top continuously.

user...I....
you don't even need the radius

1,815,520,000 cakes = Earth-Moon distance.
Each time a slice is added to the tower, the new size of the tower is the old size*1.5. This means that the number of cuts can be modeled by the equation y=1.5^x where y is the distance and x is the number of cuts made. Subbing in, 1,815,520,000=1.5^x
$\log_1.5 1,815,520,000 = 52.580696436$
So it would take 53 cuts to reach the moon.

step 1) convert distance from moon at apoapsis in km to distance from moon to cm at apoapsis.

step 2) divide by height of cake to get home many layers needed to reach the moon

step 3) since every time you cut the cake in half you multiply by two, find what power you gave to take two to to get the distance to the moon in cm /20

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Moondust is pure poison.

Fuck this thread, I am going to eat cake.

Try shooting arrows at tortoises until you understand why this will not wok.

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You don't multiply by 2, you add half of the current height to the top, so you multiply by 1.5.

you double the height each time. why would you multiply 1.5? you're not halving it? you cut all the way to the bottom after adding the previous half on top. Unless I just read it wrong.

this
implying 1.8 billion slices would get to the width of an atom

slicing the cake into 1.8B even slices would give each slice an outer width of 5.2*10^6m
Assuming cake is made out of carbon with a diameter of 2*10^-12m you would never get to the width of an atom and COULD slice the cake 1.8B times.

Every slice cuts through the whole cake, so the height doubles every time.

which is what said

Height: 20cm
Cut it in half, stack the 2 halves
Height: 40cm
Cut one half in half, stack the 3 pieces
Height: 60cm
etc etc

or maybe you meant height 20->40->80->160->360

Yeah, otherwise the question would be boring. The question might as well be "how many cakes stacked on top of each other will reach the moon"

Cake height = 20*2^n
where n = amount of slices
distance D to moon = 36,310,400,000cm

D = 20*2^n
ln(D) = ln(20)+n(ln(2))
n = (ln(D)-ln(20))/ln(2)
n = 30.7

31 Slices and you would reach the moon
inb4 im a brainlet and did something wrong

Though you actually showed your work