The Official "Math Problem of the Week" thread

Demonknightx

Demonknightx

Snoll Chef
Adventurer
Joined
Mar 19, 2005
Messages
920
Location
San Diego
FFXI
Demonknightx
FFXIV
Demon Knightx
hiya fellow QCDNers. i have a teacher for Pre-Cal that gives us a Problem of the Week to solve for fun, and sometimes extra credit.. usually they're pretty fun, so i'll post the problem on here every week and see if anyone can figure them out ^---^. here's this weeks.


Apple Pie

Angie is serving a fresh apple pie that she has baked for her family. She wishes to cut the pie into four equal pieces, but wants to do it in a creative manner. She decides to make only curved cuts with her knife, using no straight line cuts. How can Angie accomplish this?
 
Pie.jpg


Very easy. I made the stright lines to show the difference in each cut compared to a normal 4 straight cut. There is no actual single correct answer for this and probably infinite answers provided you can cut infinitely small.
 
lol yea. what math did you use to make the graph tho? the answer i came up with was the function of the squre root of X... i cant draw it on here, but its the same idea as what you posted =P
 
I did it just graphically without any actual calculations. Not even sure how I would go about making a calculation either. All I know is, any area I cut out of one pie piece has to be replaced by cutting out an equal volume of another. I also think there is some form of symmetry which must be adhered to in order to make four equal pieces, but I don't know exactly how it works. In my all 4 pieces are the same, but I can make 4 equal area slices which are not the same shape unless I flip 2 of them.

Edit: Now that I actually think about it, I think there is an easy way to do it using a radial coordinate system versus using the standard cartesian system. Again been so long since I have done this type of stuff, I can't remember much. >.>
 
Last edited:
well since this thread is here...someone wanna do this problem for me? :P

"The measure of the diagonal of a cube is 2rad6. Find the number of square units in the total surface area."
 
Tyrath said:
well since this thread is here...someone wanna do this problem for me? :P

The measure of the diagonal of a cube is 2rad6. Find the number of square units in the total surface area.
Click to expand...
700_1024.ts1158423331220.jpg

Black lines are outer edges of the cube, we'll call them "L"
Red lines are the diagonal on one of the faces of the cube, the angle is 90 degees, making them L√2
Blue line is your diagonal for the curve, let's call it D, √(L² + (L√2)²), making it C = √(3L²) = L√3
C / √3 = L
For a cube, SA = 6L²
Plugging in L, you get SA = 6 * (C / √3)² = 2C²
 
Last edited:
Lavi said:
Pie.jpg


Very easy. I made the stright lines to show the difference in each cut compared to a normal 4 straight cut. There is no actual single correct answer for this and probably infinite answers provided you can cut infinitely small.
Click to expand...

I was personally thinking cutting a hole out out the center and making three wide, "u" shaped pie pieces out of the sides, but your example is infinitely easier to explain.
 
Stouter said:
700_1024.ts1158423331220.jpg

Black lines are outer edges of the cube, we'll call them "L"
Red lines are the diagonal on one of the faces of the cube, the angle is 90 degees, making them L√2
Blue line is your diagonal for the curve, let's call it D, √(L² + (L√2)²), making it C = √(3L²) = L√3
C / √3 = L
For a cube, SA = 6L²
Plugging in L, you get SA = 6 * (C / √3)² = 2C²
Click to expand...


I followed most of that, but where'd the C come from? >.>
 
But if the Surface Area = 2C²....Whats the value of the C? I havent taken calculus and stuff yet, just trying to get this problem done for something. So confused ._.
 
Demonknightx said:
lol yea. what math did you use to make the graph tho? the answer i came up with was the function of the squre root of X... i cant draw it on here, but its the same idea as what you posted =P
Click to expand...
Dunno how'd you possibly put that to a formula >_> I guess you could try g(x) = sinx, rotate pie 90degrees, and then apply g(x) again.

something like:

g(x) = sin(x)
f(x) = sin-1(x) Or g-1(x)

would tecnhcially work, but it'd violate some rules about dividing by zero, not actually being a function, and etc...
 
Oh I see what I did, I changed D into C, replace all C's with D's. C (or D) is your center diagonal.
 
Woops missed something obvious,

f(x) = sqrt(x)
g(x) = -sqrt(-x)
h(x) = -x^3

should work
 
Daveman said:
Dunno how'd you possibly put that to a formula >_> I guess you could try g(x) = sinx, rotate pie 90degrees, and then apply g(x) again.

something like:

g(x) = sin(x)
f(x) = sin-1(x) Or g-1(x)

would tecnhcially work, but it'd violate some rules about dividing by zero, not actually being a function, and etc...
Click to expand...

You could do it as two functions:
x=siny
y=sinx

Last I checked, math teachers don't mind people putting x in terms of y instead of y in terms of x for simple solutions such as this.
 
Stouter said:
Oh I see what I did, I changed D into C, replace all C's with D's. C (or D) is your center diagonal.
Click to expand...

Oooh, I see now. Thanks a bunch
 
...........................................
..........................
JESUS.
I need an advil now...
 
Taurothar said:
You could do it as two functions:
x=siny
y=sinx

Last I checked, math teachers don't mind people putting x in terms of y instead of y in terms of x for simple solutions such as this.
Click to expand...
Thing is I really think some teachers may infact mind, old lady math teachers are the worse D: anyways it all depends, your formulas can be understood/graphed just fine, but demonkightx mentioned the word function, which is usually taught as f(x), and the domain/range things get screwy with things that fail the verticle line test.

The 3 formulas I posted afterwards should work, without any worry about breaking rules, and creates exactly the same thing lavi(?) drew.
 
Omg guys. I'm like, so grateful Demon, that you made this thread.

I was doing my homework (on functions), and read this forum. Holy hell. lol
Now I'm so god damn confused.
 
You must log in or register to reply here.
Back
Top