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1511 - 1520 of 3266 for Complex projective planeSearch Results
An equation of the form y=ax^3+bx^2+cx+d, (1) where the three roots are real and distinct, i.e., y = a(x-r_1)(x-r_2)(x-r_3) (2) = ...
An equation of the form y=ax^3+bx^2+cx+d, (1) where two of the roots of the equation coincide (and all three are therefore real), i.e., y = a(x-r_1)^2(x-r_2) (2) = ...
The evolute of the curtate cycloid x = at-bsint (1) y = a-bcost (2) (with b<a) is given by x = (a[-2bt+2atcost-2asint+bsin(2t)])/(2(acost-b)) (3) y = ...
A curve has positive orientation if a region R is on the left when traveling around the outside of R, or on the right when traveling around the inside of R.
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)
The evolute of a deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid evolute for n=3 x_e = 2cost-cos(2t) (3) y_e = 2sint+sin(2t), (4) which is ...
The involute of the deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid involute for n=3 x_i = 1/9[2cost-cos(2t)] (3) y_i = 1/9[2sint+sin(2t)], (4) ...
The radial curve of the deltoid x = 1/3a[2cost+cos(2t)] (1) y = 1/3a[2sint-sin(2t)] (2) with pedal point (x_0,y_0) is x_p = 1/6[3x+cost+3xcost-cos(2t)-3ysint] (3) y_p = ...
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