Mathematical Questions and Solutions, Τόμος 20F. Hodgson, 1874 |
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Σελίδα vi
... random so as to cut a given triangle , and two points are taken at random within the tri- angle ; find the chance that the points lie on opposite sides of the line .. ...... 3726. ( Dr. Hart . ) — Find n numbers such that if the square ...
... random so as to cut a given triangle , and two points are taken at random within the tri- angle ; find the chance that the points lie on opposite sides of the line .. ...... 3726. ( Dr. Hart . ) — Find n numbers such that if the square ...
Σελίδα ix
... random crosses a circle ; if two points are taken at random within the circle , show that the chance that they fall on opposite sides of 128 the line is 45π2 4068. ( Professor Wolstenholme , M.A . ) — A lamina moves in its own plane in ...
... random crosses a circle ; if two points are taken at random within the circle , show that the chance that they fall on opposite sides of 128 the line is 45π2 4068. ( Professor Wolstenholme , M.A . ) — A lamina moves in its own plane in ...
Σελίδα x
... taken , and equal to the square of the radius of a circle of the same area as the contour , -the distances being taken at equal angu- lar intervals . 2. Show that the mean square of the distance between two points taken at random in any ...
... taken , and equal to the square of the radius of a circle of the same area as the contour , -the distances being taken at equal angu- lar intervals . 2. Show that the mean square of the distance between two points taken at random in any ...
Σελίδα xi
... taken at ran- dom within any convex boundary , of perimeter L and area ♫ , the chance that a straight line drawn at random across the area shall pass between the two points is p 3LQ C + dp do , where C is the length of a variable chord ...
... taken at ran- dom within any convex boundary , of perimeter L and area ♫ , the chance that a straight line drawn at random across the area shall pass between the two points is p 3LQ C + dp do , where C is the length of a variable chord ...
Σελίδα xiii
... random parallel to BD . If two points are taken at random within the triangle ABC , prove ( 1 ) that the probability of their lying on opposite sides of EF is 15 2 13 ( 2 - UU1 ) ; ; where A , U , U , denote the areas of the triangles ...
... random parallel to BD . If two points are taken at random within the triangle ABC , prove ( 1 ) that the probability of their lying on opposite sides of EF is 15 2 13 ( 2 - UU1 ) ; ; where A , U , U , denote the areas of the triangles ...
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a+b+c AB² axis biquadratic equation chord circle circular point column confocal conic cos² cusps distance double tangent drawn ellipse envelope equal equation Euler's theorem G. S. CARR given hence hyperbola hypotenuse integral J. J. SYLVESTER J. L. KITCHIN JAMES COCKLE lamina line infinity locus multiplying nine-point circle obtain opposite sides P₁ parallel perpendicular plane points at infinity points of contact polygon polyhedron positive Professor CROFTON Professor WOLSTENHOLME Proposed by Professor prove Pythagorean triangles Question radii radius real asymptotes right angles right-angled triangle roots side-difference sin² sin³ Solution by Professor square number straight line Substituting taken at random theorem triangle ABC tricusped hypocycloid values Watson's whence