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The catacaustic of one arch of a cycloid given parametrically as x = t-sint (1) y = 1-cost (2) is a complicated expression for an arbitrary radiant point. For the case of the ...

The evolute of the cycloid x(t) = a(t-sint) (1) y(t) = a(1-cost) (2) is given by x(t) = a(t+sint) (3) y(t) = a(cost-1). (4) As can be seen in the above figure, the evolute is ...

The involute of the cycloid x = a(t-sint) (1) y = a(1-cost) (2) is given by x_i = a(t+sint) (3) y_i = a(3+cost). (4) As can be seen in the above figure, the involute is ...

The radial curve of the cycloid with parametric equations x = a(t-sint) (1) y = a(1-cost) (2) is the circle x_r = x_0+2asint (3) y_r = -2a+y_0+2acost. (4)

Let p be an odd prime and F_n the cyclotomic field of p^(n+1)th roots of unity over the rational field. Now let p^(e(n)) be the power of p which divides the class number h_n ...

A cylinder can be dissected into unequal squares, with nine squares required at a minimum. Trivial squarings can be constructed by taking rectangle dissections and matching ...

R_m(x,y) = (J_m^'(x)Y_m^'(y)-J_m^'(y)Y_m^'(x))/(J_m(x)Y_m^'(y)-J_m^'(y)Y_m(x)) (1) S_m(x,y) = (J_m^'(x)Y_m(y)-J_m(y)Y_m^'(x))/(J_m(x)Y_m(y)-J_m(y)Y_m(x)). (2)

The cylindrical parts of a system of real algebraic equations and inequalities in variables {x_1,...,x_n} are the terms f_1 <= x_1<=g_1 (1) f_2(x_1) <= x_2<=g_2(x_1) (2) | ...

A natural number n>3 such that n|(a^(n-2)-a) whenever (a,n)=1 (a and n are relatively prime) and a<=n. (Here, n|m means that n divides m.) There are an infinite number of ...

The symbol | most commonly used to denote the adjoint operator. The dagger is also known as the obelisk, obelus, or long cross (Bringhurst 1997, p. 275).