1 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output? With out falling How far over can.

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Presentation transcript:

1 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output? With out falling How far over can you shift it go over?

2 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output: I have produced the first i-1 objects. But if I keep adding blocks it will falling Is this a proof that it is not possible? Try again

3 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output: I have produced the last i-1 objects. Extra info: Center of mass is within bottom block Leaning distance so far Where should we put the next block? it will falling

4 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output: I have produced the last i-1 objects. Extra info: Center of mass is within bottom block Leaning distance so far Where should we put the next block? it will falling

5 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output: I have produced the last i-1 objects. Extra info: Center of mass is within bottom block Leaning distance so far Where should we put the next block? No progress

6 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output: I have produced the last i-1 objects. Extra info: Center of mass is within bottom block Leaning distance so far Where should we put the next block? With the center of mass of the above blocks teetering on the edge of supporting block.

7 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks More of the output: I have produced the last i-1 objects. Extra info: Center of mass is within bottom block Leaning distance so far Where is the new center of mass?

8 Leaning Tower Where is the new center of mass? Mass = m 2 Mass = m 1 Center of mass = r 1 Center of mass = r 2 Center of mass (Ignoring veridical)

9 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks Where is the new center of mass? Center of mass = r 1 Center of mass = r 2 Center of mass Mass = m 1 = 1 To make the math easier, lets call this zero. mass 2 mass 1 Mass = m 2 = i-1 = 0 Center of mass is 1/i from right edge of i th block.

10 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks I have produced the last i-1 objects. More of the output: Extra info: Center of mass is 1/i from right edge of i th block. Leaning distance so far? Add the next block. 1/i 1

11 Leaning Tower Output: Stack them leaning as far over as possible. Input: Lots of 2in wide blocks 1/i 1