Mathematical Snapshots by Hugo Steinhaus PDF

By Hugo Steinhaus

ISBN-10: 0195032675

ISBN-13: 9780195032673

ISBN-10: 0196317193

ISBN-13: 9780196317199

One of the most sensible three leisure math books i've got learn. a number of mathematical difficulties are tackled with a pithy variety appropriate to leisure mathematicians who are looking to transcend the lyricism of Martin Gardner.

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Example text

Thus, for a given torque, two somersaults in the pike position take almost as long as four somersaults in the tuck position. 62 somersaults in the pike position. The double somersault in the pike position is harder. 6. Angular momentum L is defined by L = Iω and the torque equation τ = Iα is more generally interpreted as “torque equals the rate of change of angular momentum” (since α is the rate of change of ω). Thus, τ ≈ ∆L/∆t. 5ωpp . A further consequence of τ ≈ ∆L/∆t is that when there is no torque, angular momentum does not change.

Picking up the story in 1970, a retired aircraft engineer named Howard Head developed tennis elbow. When he hit a tennis ball off-center, his racket would twist and put pressure on the elbow. His engineering solution was to reduce the twisting of the racket by increasing its MOI for off-center hits. 4 shows how to do it: move the mass farther from the center. In this case, most of the mass of the racket head is in the frame, so moving the frame away from the center by enlarging the racket head will increase MOI.

Calculus Box: A General Model of a Ball in Flight If you mathematically model the forces of gravity, air drag, and Magnus force, you have a highly accurate equation for the flight of a ball. You also have an equation that cannot be solved (meaning that a solution cannot be found in terms of the basic elementary functions that you commonly see in mathematics courses). In our digital age, this is not a deal-killer. We can throw the equations into Mathematica or other software and get a nice graphical “solution” that gives us important information.