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The discussion of plane sections can be performed for the unit hyperboloid of two sheets with equation : + = which can be generated by a rotating hyperbola around one of its axes (the one that cuts the hyperbola) A plane with slope less than 1 (1 is the slope of the asymptotes of the generating hyperbola) intersects either in an ellipse or in a ...
A gold foil with a thickness of 1.5 micrometers would be about 10,000 atoms thick. If the average deflection per atom is 0.008°, the average deflection after 10,000 collisions would be 0.8°. The probability of an alpha particle being deflected by more than 90° will be [62]: 109
Hyperboloid of one sheet, such as cooling towers A hyperboloid of one sheet is a doubly ruled surface , and it may be generated by either of two families of straight lines. The hyperbolic paraboloid is a doubly ruled surface so it may be used to construct a saddle roof from straight beams.
Hyperboloid structures are architectural structures designed using a hyperboloid in one sheet. Often these are tall structures, such as towers, where the hyperboloid geometry's structural strength is used to support an object high above the ground. Hyperboloid geometry is often used for decorative effect as well as structural economy.
Hyperbola: the midpoints of parallel chords lie on a line. Hyperbola: the midpoint of a chord is the midpoint of the corresponding chord of the asymptotes. The midpoints of parallel chords of a hyperbola lie on a line through the center (see diagram). The points of any chord may lie on different branches of the hyperbola.
It was proved independently by Auguste Boutin and V. Retali., [5] [6] [7] but it became famous only after Kariya 's paper. [8] Around that time, many generalizations of this result were given. Kariya's theorem can be used for the construction of the Feuerbach hyperbola. Both Lemoine's theorem and Kariya's theorem are a special case of Jacobi's ...
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Each hyperbola is defined by = / and = / (with =, =) in equation . Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity . It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola , as can be seen when graphed on a Minkowski diagram ...