The tower of hanoi is a game/ project we did in class. in the app on our ipads, we have to use the blocks to move to the third stand in the original order. After we tried, the app would tell us the actual step we need to get there. Our team tried the game for several times but always takes more steps to complete it. At the end of this game we find an equation show the pattern of this game and can we complete the game perfectly. The equation we prove out is Tn=2^n -1.
the other lesson was about mathmatical induction. This looks really complecated at first, but it is actually not when you get it. First, we need to prove true for n=1, we compare the left and right hand side. After that, we assume true for n=k, and we need to show true for k+1. In this step, we replace all the k with k+1. And we simplify. we rplace the k term with the step when we assume k=n. And we simplify the problem and we would get same things on both sides and that is thw ultimate goal.
the other lesson was about mathmatical induction. This looks really complecated at first, but it is actually not when you get it. First, we need to prove true for n=1, we compare the left and right hand side. After that, we assume true for n=k, and we need to show true for k+1. In this step, we replace all the k with k+1. And we simplify. we rplace the k term with the step when we assume k=n. And we simplify the problem and we would get same things on both sides and that is thw ultimate goal.
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