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The following is not the method Cavendish used, but describes how modern physicists would calculate the results from his experiment. [ 26 ] [ 27 ] [ 28 ] From Hooke's law , the torque on the torsion wire is proportional to the deflection angle θ {\displaystyle \theta } of the balance.
Archimedes did not admit the method of indivisibles as part of rigorous mathematics, and therefore did not publish his method in the formal treatises that contain the results. In these treatises, he proves the same theorems by exhaustion, finding rigorous upper and lower bounds which both converge to the answer required. Nevertheless, the ...
The condition that the two figures balance now allows him to calculate the total mass of the other figure. He considered this method as a useful heuristic but always made sure to prove the results he found using exhaustion, since the method did not provide upper and lower bounds.
In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height. He achieves this in one of his proofs by calculating the value of a geometric series that sums to infinity with the ratio 1/4.
An object whose weight exceeds its buoyancy tends to sink. Calculation of the upwards force on a submerged object during its accelerating period cannot be done by the Archimedes principle alone; it is necessary to consider dynamics of an object involving buoyancy. Once it fully sinks to the floor of the fluid or rises to the surface and settles ...
Most balance transfer cards charge balance transfer fees of 3 percent to 5 percent of your balance. So, if you transfer $5,000 in debt to a balance transfer card, you could pay an extra $150 to ...
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To ensure you pay off the balance before the intro period ends, make a plan using Bankrate’s credit card balance transfer calculator to determine the monthly payment amount that will help you ...