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Do you remember plastic cat's eyes, light reflectors that we attach to the bicycle wheels? Attach one adjoining the border of the wheel. The curves we obtain belong to the family of cycloids. The wheel is the cold the generating disk (or circle) of the cycloid. But let's return to our century and take use modern technique. There is a stone on the bikes way that in the wheels tread.
In what direction will it fly after several turns when it leaves the tread? In the direction of the bike in the opposite? As we know, the motion should start tangent to its old trajectory. A tangent to a cycloid has always the same direction as the bike and through the top point of the generating circle. It will fly in the same direction. You may ask about the stones thrown into the windscreen the following car. These are, in fact, those that have been thrown immediately without rotating with the wheel.
Do you remember driving your bicycle over the puddles without a back wing in your childhood? A wet stripe on your back was an every-day confirmation of this result. The XVII century is the century of the cycloid. The best scientists were studying its properties. Which trajectory moves a body with gravitation acting on it for one point to another in the? This was one of the first problems of the branch of science which is now called variational calculus.
Cycloid Macular Edema
Fotor photo editor for mac. One can minimize (or maximize) different parameters: the length of a path, speed, time. The problem of brachistochrone is to minimize time (which is accentuated by the name: brachistos means the shortest, and chronos means time in Greek). The first that comes to mind is a trajectory. Let's also consider a with the cuspidal point in the upper of two given points. And, following Galileo Galilei, a — connecting our points. Build of this shapes and watch which of the bobsleigh comes the first.
The history of bobsleighing rises to Switzerland. In 1924 in a french town Shamonie the First Winter Olympics take place. The have already bobsleighing competitions included for couples and quadruples. The only year when a bobsleighing team consisted of 5 persons was 1928.
Since then only teams of two and four men compete. There is a lot of interesting in the bobsleighing rules.
Of course, there is a limit on the bobsleigh weight, but there are even limitations on the materials one can use in bobsleigh blades (the front pair of them is connected to the wheel and the back pair is fixed). For example, one can not use radium to make his blades.
Let's start our quadruples. Which of the bobsleighs comes the first? The green one, sponsored by Mathematical etudes, on the cycloidal track! Why Galileo Galilei considered a quarter of a circle as the best trajectory in the sense of timing? He was inscribing polylines in it and mentioned that increasing the number of edges decreases the time of descent.
This is how Galilei naturally came to a circle but made a wrong conclusion that this trajectory is the best among all the others. As we've seen, the best one is a cycloid. One can draw a cycloid passing through two give points such that the upper of them is a cuspidal point of the cycloid.
Even when the cycloid has to grow up in order to pass through the second point, it remains the! Another beautiful problem connected to the cycloid is the problem of tautochrone. In Greek tauto means equal, and as we already know, chronos means time. Build three similar cycloid-shaped slides so that the end of the slide is the. Put three bobsleighs on and let them go. An amazing fact is that all of them will! In winter you can build a slide of ice and check this property yourself!