January 23, 2011

• Take some square sheets of paper (e.g. post it notes), and a board pin. Arrange first 3 sheets, so that they cover the maximum possible area, and each of them is supported by the single board pin. Try this with 4 sheets. Now comes the interesting part:  what will happen when you have 5 sheets, 6 sheets, ... 100 sheets?  How should the arrangement of these papers should  look like - just supported by a single board pin?
• Viviani's Theorem: Consider an equilateral triangle, and take a point anywhere in its interior. Calculate the distance from this point to each of the sides of the triangle, and look at the sum of these distances. Take another point, and do the same calculation. Wow - both the sums are the same! In fact this is same as the height of this triangle!  Will some similar statement be true for other regular shape figures - like a square or a hexagon.
• Take a soccer ball, and tie the rope along its equator. Lets say a superhuman did the same way around earths equator. Now we want to make the rope bit relaxed - say we want to ensure that the distance between the ball (as well as Earth) and rope is at least 5 cms. Whats the additional length of the rope we need for the ball and for Earth?  (Earths radius is approximately 6350 Kms.)
• We will do some Sangaku Geometric Art shapes - for example three circles tangent to the same line etc.