Mathemagic!! Soma Dutt
Have you heard about Radhanath Shikdar? Radhanath Shikdar was a mathematician from Bengal who measured the height of peak XV of Himalayas, which was later named as Mt. Everest, the tallest peak over sea level. He did the calculations without ever climbing the peak. Have you ever wondered how? (1813– 1870)
How do you measure the depth of seas? Echosounders have been used to determine depth of oceans. Echosounders are attached to the hull of a ship or a towed vehicle. It sends an outgoing sound pulse into the water. The sound energy hits the bottom after travelling through the water of the ocean, and is reflected back towards the source, where it is received, and recorded. The time that it takes for sound to make the round trip to the seafloor and back is measured. Water depth is determined from the travel time and the speed of sound in water.
These are some more problems for you… • How do you calculate your distance from lightening? • How do you calculate your distance from the horizon? • How do you calculate the heights of big trees/monuments in your city? • How can you use your body/body parts to measure the furniture you are buying for your new house?
All these problems can be solved by Mathemagic!! By simple applications of formulas.
One example: How to measure a tree • • • Select a straight tree in your locality. Stand far enough from the tree so that you can see the whole tree—top to bottom—without having to move your head. Stand at level with the ground at the tree’s base. Ensure that your view is unobstructed. Have a friend stand near the tree. Hold a pencil or a small, straight stick in one hand stretch your arm out so that the pencil is at arm’s length in front of you (between you and the tree). Close one eye and move the pencil up or down so that you can sight the very top of the tree at the top of the pencil.
• Move your thumb up or down the pencil so that the tip of your thumbnail is aligned with the tree’s base. While holding the pencil in position so that the tip is aligned with the tree’s top (as in step 3), move your thumb to the point on the pencil that covers the point where the tree meets the ground. • Rotate your arm so that the pencil is horizontal (parallel to the ground). Keep your arm held straight out, and make sure your thumbnail is still aligned with the tree’s base. • Have your friend move so that you can sight his or her feet “through” the point of your pencil. That is, your friend’s feet should be aligned with the pencil’s tip. He or she may need to move backward, sideways, or diagonally. Since, depending on the height of the tree, you may need to be some distance away from your friend, you might have to use hand signals to give him/her instructions. • Measure the distance between your friend and the tree. Have your friend remain in the place or mark the spot with a stick or rock. Then measure the straight-line distance between that spot and the base of the tree. The distance between your friend and the tree is the height of the tree.
Your Work • To start with, select 3 monuments in your city. • Figure out how you could measure their heights. (Hints: try using your previous knowledge of ratio proportion) • Do fieldwork , if necessary. • After calculations, verify your results. • Use graph to draw comparisons.
Share your work • On Powerpoint presentation • On wiki/blog
Acknowledgements • en. wikipedia. org • http: //www. wikihow. com
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