Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20060501 06:09:20
tetherballI think I just came up with one of the toughest math problems ever. Last edited by mikau (20060501 06:15:39) A logarithm is just a misspelled algorithm. #2 20060501 06:34:40
Re: tetherballI think the reason I'm having such difficulty trying to work this out is that you can't really find an angle to locate the ball from. Its not pivoting around the center of the poll and moving in, its pivoting around the edge of the poll its touching which is contstantly changing. So you really can't truely say its rotating around anything. A logarithm is just a misspelled algorithm. #3 20060501 08:05:55
Re: tetherballAll right, this is getting interesting. It might be a good idea to define the angle as the point of tangency of the string to the poll, in relation to its center. At each exact point, the string will be hinging on the point of tangency which will be perpendicular to the radius at that point, and its path will be that of a circle rotating about the point of tangency. Last edited by mikau (20060501 08:10:48) A logarithm is just a misspelled algorithm. #4 20060501 08:30:58
Re: tetherballIts just that arc length is tricky. For instance you could use inscribed rectangles that look like a staircase to approximate the area under a curve, as the rectangles get smaller the area approximation gets closer, and the "staircase" looks more and more like the line. But if you try to find the length of the line by summing the horizontal and vertical faces of the steps your going to be way off. You need the pythagorean theorem to take into account movement in both dimensions. A logarithm is just a misspelled algorithm. #5 20060501 09:14:17
Re: tetherballThe plot thickens.. Last edited by mikau (20060501 09:17:29) A logarithm is just a misspelled algorithm. #6 20060501 10:18:00
Re: tetherballWell assuming thats right, the answer should be about 380.2 inches. I need to see if I can write a program to approximate it using a reliable method. Last edited by mikau (20060501 14:44:21) A logarithm is just a misspelled algorithm. #7 20060502 03:53:26
Re: tetherballWell I think I know where my mistake is. If I had found the objects exact direction of movement at a precise moment in time it would work. But the object isn't just hinging on the point of tangency, the radius is also changing and the hinging point is also changing. All the changes in movement must be taken into account to find its exact direction in a point in time. The reason it worked with the circle expermient was that we were going in the precise direction at each moment in time. A logarithm is just a misspelled algorithm. 