Description:
Recreational Geometry Problems. (Moderated)
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What would be the vollume be ?
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Suppose - (instad of a square with 10 units side) we have a cube with a 10 units side, and each of its 8 corners is the centre of a 10 unit radius sphere, can we find the volume that is common to all of the spheres ?
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Water in a tank
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A cylindrical tank with its axis horizontal has a nozzle at the bottom. The tank is full at first, and it is found that it takes 3 minutes for half the water to flow out. If the radius of the tank is 2 ft. and its length is 8 ft. find the depth of the water after t minutes. Find also the time t for the tank to empty.... more »
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3d Circumcircle problem
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There are 3 lines in 3d space given by their parametric equations in [x,y,z] coordinates: (a) [75/13*r, 4, 180/13*r + 52/5] (b) [33/13*s, 56/5*s + 1388/165, 396/65*s + 52/5] (c) [-42/13*t, 56/5*t + 308/15, -504/65*t + 52/5] Find out if these lines intersect or not. If they do intersect, do the... more »
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Inscribed circle
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Find the equation of the inscribed circle of the triangle formed by the lines 4x-3y+9 = 0 12x+5y-43 = 0 and 7x+24y+19 = 0
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Parabola: Finding the next point?
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Assume that I have a parabola y = 4ax^2. Lets say that I start at point (x,y). How to find the next point (xk,yk) such that the distance between the two points is of length k. I'd somehow want to generate n such consecutive points. Any ideas?
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Parallelogram area
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Find the two values of f for which the equation 8x^2 + 6xy - 5y^2 + 4x + 2fy - 4 = 0 represents straight lines. Find the area of the parallelogram formed from the four lines so obtained.
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Perpendicular lines
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Show that the lines joining the origin to the intersections of the line 4x-y-17 = 0 and the curve 2x^2+2y^2-20x+5y+17 = 0 are perpendicular.
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