## View Poll Results: What is the hardest math you learned?

Voters
105. You may not vote on this poll

38 36.19%
• Trigonometry

11 10.48%
• (Enriched) Geometry

11 10.48%
• Equations (specify)

4 3.81%
• Graphing Equations (specify)

2 1.90%
• Basic Algebra (specify)

7 6.67%
• I can do better!

24 22.86%
• What kind of math is that?!

8 7.62%

1. Originally Posted by IanTheCuber
Pascal's Triangle FTW

[...]

I think a similar method can be applied to Fibonacci Sequence, eh?
Not exactly. I mean it's even more simple to apply Pascal's Triangle to calculate the Fibonacci numbers: you don't have to adjust the pascal's triangle at all. Just look at Wikipedia. They show that

and they show this image which represents that:

2. I just wanted to make it more "in depth"

3. ## A Problem I'm Not Quite Sure How To Solve

I got some errors that look like this:
Warning: touch() [function.touch]: Utime failed: Permission denied in [path]/includes/class.latex-vb.php on line 167

Warning: touch() [function.touch]: Utime failed: Permission denied in [path]/includes/class.latex-vb.php on line 167

Warning: touch() [function.touch]: Utime failed: Permission denied in [path]/includes/class.latex-vb.php on line 167

Anyways, that's not the problem I have for you guise.

Backstory: So there's this game my friend Shiaohan showed me in middle school involving a shuffled deck of cards. It was a pretty stupid game, looking back, but the gameplay was simple--draw the top card off the deck, turn it over on the table, and say "Ace."
If the card is an Ace, you get zero points, your game is over, and you must shuffle the cards and start over from zero points.
If the card isn't an Ace, you get one point, and you repeat the process of drawing cards, each successive time proclaiming the next value ("Two", "Three",... "King", and wrap around to "Ace" again), racking up as many points as you can before you have to start over.
The goal is to get 52 points, aka going through the entire deck without fail.
It quickly occurred to me that you can troll this game by having a sorted deck of cards and then placing one card from the top to the bottom. In this way, the result obviously comes out to 52 points, even if the deck wasn't completely shuffled.
Problem: What is the probability of playing this game and receiving a result of 52 points?

4. Originally Posted by Ranzha V. Emodrach
I got some errors that look like this:
Warning: touch() [function.touch]: Utime failed: Permission denied in [path]/includes/class.latex-vb.php on line 167

Warning: touch() [function.touch]: Utime failed: Permission denied in [path]/includes/class.latex-vb.php on line 167

Warning: touch() [function.touch]: Utime failed: Permission denied in [path]/includes/class.latex-vb.php on line 167

Anyways, that's not the problem I have for you guise.

Backstory: So there's this game my friend Shiaohan showed me in middle school involving a shuffled deck of cards. It was a pretty stupid game, looking back, but the gameplay was simple--draw the top card off the deck, turn it over on the table, and say "Ace."
If the card is an Ace, you get zero points, your game is over, and you must shuffle the cards and start over from zero points.
If the card isn't an Ace, you get one point, and you repeat the process of drawing cards, each successive time proclaiming the next value ("Two", "Three",... "King", and wrap around to "Ace" again), racking up as many points as you can before you have to start over.
The goal is to get 52 points, aka going through the entire deck without fail.
It quickly occurred to me that you can troll this game by having a sorted deck of cards and then placing one card from the top to the bottom. In this way, the result obviously comes out to 52 points, even if the deck wasn't completely shuffled.
Problem: What is the probability of playing this game and receiving a result of 52 points?
I think it would just be

5. Originally Posted by ben1996123
I think it would just be
Um, no.

6. Originally Posted by Ranzha V. Emodrach
Um, no.
oh yeah. i just realised it's a deck of cards.

7. Originally Posted by ben1996123
oh yeah. i just realised it's a deck of cards.

facehoof
It's okay xD

I think it's more of a binary pass/fail intuition system that I have to figure out.

8. So over lunch I thought of this problem, and instead of solving it with just, the volormula of a sphere I decided to have a crack at integration. Of course, being me, I accidentally did it for a cylinder, not a sphere. So I chatted to ben about rotating it about the x axis, because I forgot how to do it and didn't think of doing it, and yeah here's the solutions.

He brought up another interesting point about chopping the sphere into n segments. Anyway enough build up:
question:
Ok so, if you have a perfectly spherical meatball and want to chop it into four equal volumed pieces with only 3 vertical, parallel cuts, where would the cuts need to be?

solution:
So I tried writing without my tablet. I integrated the equation which is a semicircle because implicits annoy me.

--
this is where I made a boo boo and assumed it was a cylinder.
I said okay so let's set this to -pi/8 and solve for x to get like -0.404
Spoiler:

silly me.
--
So anyways I chatted to ben about it and he reminded me of revolving around the x axis and finished it
[18:17:28] Bacon: or you could use the volume of a sphere formula
[18:17:32] fivebldcubing: but thats boring
[18:17:35] Bacon: kso
[18:17:44] Bacon: you have y=√1-x²
[18:18:02] Bacon: imagine that curve rotated τ radians around the x axis to form a sphere
[18:18:05] Bacon: k?
[18:18:24] fivebldcubing: yeah
[18:18:32] Bacon: to get the volume of that
[18:18:38] Bacon: integrate pi y² dx
[18:18:56] Bacon: so pi*integral 1-x²dx from -1 to 1 = volume
[18:19:13] Bacon: =pi[x-x³/3] from -1 to 1
[18:19:19] Bacon: =4pi/3

so whole volume = 4pi/3
[18:21:09] Bacon: so each piece volume = pi/3
[18:21:36] Bacon: so integrate pi y² dx from -1 to n = pi/3
[18:21:49] Bacon: integrate y² dx from -1 to n = 1/3
[18:21:58] Bacon: etc
[18:22:06] Bacon: replace n with x because n is stupid
[18:22:18] Bacon: multiply by 3 to get rid of fractions n stuff
[18:22:27] Bacon: and you get x³-3x-1=0
[18:22:38] Bacon: and the solution is -0.347296etc.

the other cuts are at 0 and +0.347296 of course.

then we talked about chopping into more/fewer pieces. Weirdly it turns out than for -1<=x<=1 one of the cuts should be

Any thoughts?

9. I'm hungry as ****, but s'graven haeg dude.

10. Anyone care to help me figure these two problems out from Abstract Algebra I?

If a|(b + c) and gcd(b, c) = 1, prove that gcd(a, b) = 1 = gcd(a, c).

and

Show that if n lines are drawn on the plane so that none of them are parallel, and so that
no three lines intersect at a point, then the plane is divided by those lines into (n^2+n+2)/2 regions.

The second one, I simply have no idea how to approach it. We've done nothing similar to this that I can recall.
The first one, we've done stuff similar, but I'm not sure how to start it. Help me just start this one?
Thanks

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