Superpolymath's 4 Ridiculously Hard Math Problems

[Super Polymath]

Lol, testing how smart the smartest forum on earth is.

https://m.youtube.com/watch?v=IHypPouflvQ

 

To summarize these 4 questions (Questions C and D had to be fixed so don't pay the video any mind for those questions):

 

1. What is the number of pennies you'd need to add to this penny spiral for it to touch the x-axis two more times, reduced by 50 pennies?

 

2. If this penny spiral reaches 12,544 pennies, how many pennies (not including the zero point) touch the x-axis?

 

3. What is the polar equation of this logarithmic spiral if each penny is equal to (1/5)^-3 square units on this coordinate plane?

 

4. a. How many more pennies would you need for the outer-most spiral-arm of this to encircle the circumference of the earth?

b. What would be the parametric equation of the resulting conical spiral if each penny represents (1/5)^-3 square units on a 3D coordinate plane?

 

For question 4 or D, originally, I made a mistake in assuming that if it encircled the earth twice it would invert into a spherical double-helix type structure, but as a logarithmic spiral, arms on the other side of the equator would continue to stretch out further and the shape would no longer remain spiral-like. Opens the door for an even more menacing question 5\E though. :)

 

And the last one is very difficult.

 

In order to answer these; please watch and pause the video to get a good look at the spiral and x y coordinate plane that I constructed, because you'll need to count the pennies, discern patterns, etc.

 

I'll tell you if your answer proves incorrect. ;) Then I will show you the dark side...I mean show you how to get an accurate answer.

 

EDIT, if you can play chess without a board in private messages, I'll play you in chess too.

 

EDIT #2: I'd advise using Mathematica for question D as in D---.

Edited August 9, 2016 by Super Polymath

[Super Polymath]

It's just made aware to me that these problems are of calculus not algebra. I've only done algebra, the person said that spirals are non-linear so this was a caclcus classification of problems because they require calculative solutions. So in just playing with pennies I've invented calculus by virtue of teaching it to myself.

 

So, my IQ is probably comparable to Isaac Newtons! ;)

Edited August 7, 2016 by Super Polymath

[LaurieAG]

You may want to summarise your 4 problems in the OP instead of just posting an external link. 

[sanctus]

Yeah, I got to 1min in the video, it is so crappy that I do not survive till he eventually says what the question is...

[Super Polymath]

You may want to summarise your 4 problems in the OP instead of just posting an external link.

 

The OP has been edited. The C and D questions needed revisions anyway. :) Edited August 9, 2016 by Super Polymath

[Super Polymath]

If anyone cares to answer anything past question #2, I've solved one and two, I will be unable to get back to you until autumn, I'll be preoccupied with college.

Edited August 23, 2016 by Super Polymath

[freeztar]

I'll go ahead and guess 15 for #1. 

 

The first axis is passed at 7 pennies, as is the next. Since the spiral veers away, it looks like it will take twice as many. Since there are only six pennies since the last axis was traversed, I am going with a gut feeling of twice as many (+1). I would imagine this pattern would repeat along this path (basically a squared equation). But I could totally be wrong. lol