## Application of Calculus - Problems and Solutions by S. Bandyopadbyay, S. Maiti PDF

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H/. Finally, the set of small resistance BQ is constructed in such a way that particles reflected from it do not hit B 0 . 1/; ı ! 0. t u The topic of this section will be continued in Chap. 2). 3 Bodies Modified in a Neighborhood of Their Boundary Here we show that a convex body can be “modified” in a small neighborhood of its boundary so that the resulting body displays an arbitrarily small resistance to the parallel flow of particles falling on it. Let us first provide an “astronautical” interpretation of the problem.

Finally, to the rectangles …C and … we assign the inscribed trapezoids V C and V such that the midpoints of two sides of these rectangles, AC and A , are also midpoints of smaller bases of length 2"3 of the trapezoids, and the opposite sides of the rectangles coincide with the larger bases of the trapezoids. If the obtained figures (rectangles, sectors, and trapezoids) do not mutually intersect, then their union is an "-channel. It will be called a channel generated by the given "-contour. 3 Consider two plane convex bodies C1 and C2 .

It is unknown, however, if there exist perfect retroreflectors that use only reflection of light rays, that is, billiard retroreflectors. Instead, we construct in two dimensions several asymptotically perfect billiard retroreflectors, that is, families of bodies whose reflective properties approach the property of retroreflection. The reflective properties of connected two-dimensional bodes are derived from the properties of hollows on their boundary; therefore, we concentrate on constructing hollows.