Happy Valentine's Day!!

Harry_the_cat

Senior Member
What do you get if you graph these parametric equations?

$$\displaystyle x = 16 sin^3(t)$$

and

$$\displaystyle y = 13 cos(t) - 5 cos(2t) - 2 cos(3t) - cos(4t)$$

Otis

Senior Member
Yours looks better than this one (from a recent thread about a quadratic function and its inverse):

$$\displaystyle f(x) = 1 - 2x - x^2 \quad\quad \text{Doma}\text{in: } \bigg[-\frac{3}{2} - \frac{\sqrt{13}}{2} \text{ , } -\frac{3}{2} + \frac{\sqrt{13}}{2}\bigg]$$

$$\displaystyle g(x) = -1 - \sqrt{2 - x} \quad\quad \text{Doma}\text{in: } \bigg[-\frac{3}{2} - \frac{\sqrt{13}}{2} \text{ , } 2\bigg]$$

$$\displaystyle h(x) = -1 + \sqrt{2 - x} \quad\quad \text{Doma}\text{in: } \bigg[-\frac{3}{2} + \frac{\sqrt{13}}{2} \text{ , } 2\bigg]$$

Denis

Senior Member
Hearty day: celebrating nail event! (9)

Otis

Senior Member
Text Rebus

TV a LINE STAY (2)

Last edited by a moderator:

mmm4444bot

Super Moderator
Staff member
Another parametric, curvy thing.

Each axis: [-2000, 2000]

Parameter t: [0, 60∙Pi]

x(t) = ((-33/2 *sin(11/7 - 7*t) - 29/5 *sin(3/2 - 6*t) - 42/5 *sin(11/7 - 5*t) - 2442/5 *sin(11/7 - t) + 1073/5 *sin(2*t + 11/7) + 434/11 *sin(3*t + 8/5) + 273/4 *sin(4*t + 8/5) + 22/5 *sin(8*t + 11/7) + 19/5 *sin(9*t + 13/8) + 90/13 *sin(10*t + 8/5) + 5/4 *sin(11*t + 11/7) - 2019/10)*Heaviside(59*Pi - t)*Heaviside(t - 55*Pi) + (-18/5 *sin(14/9 - 11*t) - 51/7 *sin(11/7 - 10*t) - 49/9 *sin(11/7 - 9*t) - 7/3 *sin(14/9 - 6*t) - 85/3 *sin(11/7 - 5*t) - 50/3 *sin(11/7 - 4*t) - 1819/7 *sin(11/7 - t) + 1733/8 *sin(2*t + 11/7) + 170/3 *sin(3*t + 8/5) + 2/3 *sin(7*t + 9/5) + 1/6 *sin(8*t + 2/3) + 2404/7)*Heaviside(55*Pi - t)*Heaviside(t - 51*Pi) + (-6/7 *sin(11/7 - 10*t) - 3 *sin(11/7 - 9*t) - 79/6 *sin(11/7 - 6*t) - 2969/8 *sin(11/7 - t) + 191/6 *sin(2*t + 33/7) + 152/7 *sin(3*t + 33/7) + 107/5 *sin(4*t + 33/7) + 13/8 *sin(5*t + 11/7) + 2/7 *sin(7*t + 23/5) + 22/5 *sin(8*t + 33/7) + 13/4 *sin(11*t + 33/7) + 3085/6)*Heaviside(51*Pi - t)*Heaviside(t - 47*Pi) + (-7/4 *sin(3/2 - 10*t) - 37/8 *sin(3/2 - 9*t) - 373/9 *sin(11/7 - 4*t) - 267/4 *sin(11/7 - 2*t) - 3133/7 *sin(11/7 - t) + 541/5 *sin(3*t + 8/5) + 820/11 *sin(5*t + 8/5) + 47/6 *sin(6*t + 12/7) + 35/3 *sin(7*t + 8/5) + 10/3 *sin(8*t + 12/7) + 5/11 *sin(11*t + 1) + 942)*Heaviside(47*Pi - t)*Heaviside(t - 43*Pi) + (-49/11 *sin(11/7 - 24*t) - 35/8 *sin(3/2 - 22*t) - 29/4 *sin(3/2 - 18*t) - 40/9 *sin(4/3 - 17*t) - 13/3 *sin(11/7 - 14*t) - 94/7 *sin(13/9 - 13*t) - 141/4 *sin(3/2 - 12*t) - 31/16 *sin(16/11 - 11*t) - 792/5 *sin(14/9 - 8*t) - 17/7 *sin(3/5 - 7*t) - 239/3 *sin(14/9 - 6*t) - 734/5 *sin(11/7 - 5*t) - 535/7 *sin(14/9 - 4*t) - 473/6 *sin(11/7 - 3*t) - 219/8 *sin(11/7 - 2*t) + 89 *sin(t + 33/7) + 1861/19 *sin(9*t + 8/5) + 603/10 *sin(10*t + 13/8) + 83/8 *sin(15*t + 5/3) + 13/4 *sin(16*t + 14/3) + 31/8 *sin(19*t + 8/5) + 26/7 *sin(20*t + 14/3) + 14/15 *sin(21*t + 7/6) + 3/4 *sin(23*t + 5/4) + 9944/13)*Heaviside(43*Pi - t)*Heaviside(t - 39*Pi) + (-104/3 *sin(4/7 - t) + 2 *sin(2*t + 20/7) + 1629/2)*Heaviside(39*Pi - t)*Heaviside(t - 35*Pi) + (-19/5 *sin(5/9 - 2*t) - 349/8 *sin(2/5 - t) + 5581/4)*Heaviside(35*Pi - t)*Heaviside(t - 31*Pi) + (-760/9 *sin(5/6 - t) + 12/13 *sin(2*t + 49/16) + 1377/7)*Heaviside(31*Pi - t)*Heaviside(t - 27*Pi) + (-9 *sin(1/8 - 2*t) - 827/9 *sin(2/5 - t) + 75/8 *sin(3*t + 25/12) - 3133/12)*Heaviside(27*Pi - t)*Heaviside(t - 23*Pi) + (41 *sin(t + 2/7) + 26/7 *sin(2*t + 19/18) + 9/2 *sin(3*t + 1/2) + 11/5 *sin(4*t + 25/8) - 4065/7)*Heaviside(23*Pi - t)*Heaviside(t - 19*Pi) + (-17/6 *sin(1/15 - 2*t) - 276/5 *sin(5/4 - t) + 2764/5)*Heaviside(19*Pi - t)*Heaviside(t - 15*Pi) + ((1234 *sin(t))/7 + 43/7 *sin(2*t + 14/3) + 54/7 *sin(3*t + 23/9) + 44/7 *sin(4*t + 5/4) + 3721/5)*Heaviside(15*Pi - t)*Heaviside(t - 11*Pi) + (-14/3 *sin(7/8 - 53*t) - 7 *sin(5/4 - 52*t) - 6 *sin(10/7 - 45*t) - 9/10 *sin(7/13 - 43*t) - 62/9 *sin(1/6 - 37*t) - 151/9 *sin(1/2 - 33*t) - 22/5 *sin(3/2 - 31*t) - 38/11 *sin(14/9 - 30*t) - 21/2 *sin(11/10 - 27*t) - 44/5 *sin(9/8 - 25*t) - 201/8 *sin(6/5 - 24*t) - 12 *sin(3/4 - 21*t) - 404/13 *sin(11/7 - 18*t) - 375/7 *sin(1/2 - 13*t) - 65 *sin(4/3 - 8*t) - 262/3 *sin(2/3 - 5*t) + 41/9 *sin(26*t) + 2406/5 *sin(t + 31/7) + 2743/8 *sin(2*t + 11/9) + 1248/7 *sin(3*t + 3/5) + 861/10 *sin(4*t + 4/5) + 197/6 *sin(6*t + 3/4) + 918/11 *sin(7*t + 30/7) + 233/3 *sin(9*t + 7/2) + 126/5 *sin(10*t + 18/5) + 397/9 *sin(11*t + 2/7) + 391/8 *sin(12*t + 1/15) + 211/7 *sin(14*t + 22/7) + 1037/14 *sin(15*t + 13/5) + 239/8 *sin(16*t + 19/8) + 209/4 *sin(17*t + 2) + 5/6 *sin(19*t + 25/9) + 207/7 *sin(20*t + 11/6) + 137/8 *sin(22*t + 13/6) + 38/5 *sin(23*t + 75/19) + 121/9 *sin(28*t + 15/7) + 73/7 *sin(29*t + 19/8) + 51/10 *sin(32*t + 8/5) + 11/5 *sin(34*t + 31/10) + 13 *sin(35*t + 27/8) + 52/5 *sin(36*t + 101/25) + 6 *sin(38*t + 11/5) + 125/14 *sin(39*t + 3) + 27/7 *sin(40*t + 2/5) + 55/4 *sin(41*t + 87/22) + 39/7 *sin(42*t + 3/4) + 31/4 *sin(44*t + 1/2) + 51/8 *sin(46*t + 93/23) + 29/14 *sin(47*t + 4) + 49/9 *sin(48*t + 26/9) + 7/5 *sin(49*t + 22/5) + 29/5 *sin(50*t + 29/10) + 70/9 *sin(51*t + 46/15) + 14/5 *sin(54*t + 3/4) - 2201/5)*Heaviside(11*Pi - t)*Heaviside(t - 7*Pi) + (-103/34 *sin(10/11 - 21*t) - 7/4 *sin(2/5 - 17*t) - 104/15 *sin(1/10 - 15*t) - 20/3 *sin(1/4 - 10*t) - 593/5 *sin(1/3 - 4*t) - 239/3 *sin(16/17 - 2*t) + 2113/7 *sin(t + 10/7) + 151/4 *sin(3*t + 8/7) + 183/4 *sin(5*t + 4/3) + 52/3 *sin(6*t + 11/5) + 115/7 *sin(7*t + 28/9) + 94/11 *sin(8*t + 19/5) + 280/13 *sin(9*t + 68/23) + 29/6 *sin(11*t + 1/2) + 59/9 *sin(12*t + 19/7) + 47/7 *sin(13*t + 12/5) + 41/6 *sin(14*t + 4/5) + 28/5 *sin(16*t + 3/7) + 9/7 *sin(18*t + 1/2) + 9/5 *sin(19*t + 7/2) + 44/15 *sin(20*t + 30/7) + 5/3 *sin(22*t + 9/5) - 9793/9)*Heaviside(7*Pi - t)*Heaviside(t - 3*Pi) + (-8/5 *sin(2/3 - 41*t) - 4/3 *sin(2/7 - 39*t) - 11/6 *sin(17/11 - 35*t) - 53/7 *sin(14/13 - 23*t) - 144/7 *sin(3/7 - 11*t) - 97/5 *sin(3/2 - 8*t) - 158/3 *sin(5/6 - 7*t) - 503/12 *sin(5/7 - 4*t) - 221/3 *sin(11/10 - 3*t) + 6521/5 *sin(t + 33/32) + 3023/6 *sin(2*t + 12/5) + 325/7 *sin(5*t + 17/5) + 307/11 *sin(6*t + 19/7) + 614/15 *sin(9*t + 23/6) + 67/4 *sin(10*t + 19/9) + 110/3 *sin(12*t + 49/12) + 105/4 *sin(13*t + 31/9) + 15 *sin(14*t + 30/7) + 324/11 *sin(15*t + 17/5) + 31/3 *sin(16*t + 26/7) + 59/3 *sin(17*t + 37/12) + 77/5 *sin(18*t + 3/2) + 15/2 *sin(19*t + 11/5) + 209/14 *sin(20*t + 4/9) + 55/9 *sin(21*t + 23/6) + 39/4 *sin(22*t + 10/7) + 137/13 *sin(24*t + 9/5) + 19/3 *sin(25*t + 1/22) + 3/2 *sin(26*t + 9/2) + 73/24 *sin(27*t + 16/9) + 15/8 *sin(28*t + 4/3) + 9/2 *sin(29*t + 23/6) + 143/18 *sin(30*t + 2) + 43/14 *sin(31*t + 14/13) + 5/4 *sin(32*t + 4/5) + 3/4 *sin(33*t + 2/3) + 13/8 *sin(34*t + 5/4) + 34/33 *sin(36*t + 21/10) + 5/8 *sin(37*t + 13/5) + 5/3 *sin(38*t + 9/7) + 11/8 *sin(40*t + 1) + 39/38 *sin(42*t + 16/7) + 16/7 *sin(43*t + 10/9) - 71/3)*Heaviside(3*Pi - t)*Heaviside(t + Pi))*Heaviside(sqrt(signum(sin(t/2))))

vBulletin can't handle it all; continued in next post …

mmm4444bot

Super Moderator
Staff member
y(t) = ((-24/5 *sin(11/7 - 10*t) - 17/5 *sin(3/2 - 9*t) - 143/6 *sin(11/7 - 8*t) - 87/4 *sin(11/7 - 6*t) - 275/23 *sin(14/9 - 4*t) - 394/3 *sin(11/7 - 3*t) - 1563/10 *sin(11/7 - 2*t) - 865/27 *sin(11/7 - t) + 647/34 *sin(5*t + 8/5) + 2/7 *sin(7*t + 4/7) + 13/5 *sin(11*t + 8/5) + 545)*Heaviside(59*Pi - t)*Heaviside(t - 55*Pi) + (-77/6 *sin(11/7 - 10*t) - 49/24 *sin(10/7 - 9*t) - 277/8 *sin(11/7 - 6*t) - 73/7 *sin(14/9 - 5*t) - 2385/7 *sin(11/7 - 2*t) - 1005/7 *sin(11/7 - t) + 230/7 *sin(3*t + 11/7) + 175/6 *sin(4*t + 33/7) + 12/7 *sin(7*t + 3/2) + 104/11 *sin(8*t + 33/7) + 7/4 *sin(11*t + 13/8) + 2691/2)*Heaviside(55*Pi - t)*Heaviside(t - 51*Pi) + (-94/11 *sin(11/7 - 6*t) - 68/3 *sin(11/7 - 4*t) - 116/5 *sin(11/7 - 2*t) + 98/3 *sin(t + 33/7) + 306/7 *sin(3*t + 11/7) + 107/7 *sin(5*t + 11/7) + 46/7 *sin(7*t + 11/7) + 53/13 *sin(8*t + 33/7) + 27/14 *sin(9*t + 11/7) + 1/9 *sin(11*t + 8/5) + 3367/4)*Heaviside(51*Pi - t)*Heaviside(t - 47*Pi) + (-70/23 *sin(7/5 - 11*t) - 23/4 *sin(17/11 - 10*t) - 75/7 *sin(17/11 - 8*t) - 31/8 *sin(10/7 - 7*t) - 122/7 *sin(3/2 - 5*t) - 329/3 *sin(14/9 - 4*t) - 390/11 *sin(20/13 - 3*t) - 753/7 *sin(11/7 - 2*t) + 385/3 *sin(t + 11/7) + 61/3 *sin(6*t + 8/5) + 57/7 *sin(9*t + 8/5) + 6733/12)*Heaviside(47*Pi - t)*Heaviside(t - 43*Pi) + (-17/7 *sin(3/2 - 17*t) - 57/4 *sin(19/13 - 12*t) - 244/9 *sin(3/2 - 11*t) - 449/7 *sin(11/7 - 7*t) - 611/11 *sin(11/7 - 5*t) - 1581/14 *sin(11/7 - 3*t) - 341/5 *sin(11/7 - t) + 223/16 *sin(2*t + 11/7) + 144/7 *sin(4*t + 11/7) + 410/3 *sin(6*t + 8/5) + 4537/42 *sin(8*t + 8/5) + 874/7 *sin(9*t + 8/5) + 118/7 *sin(10*t + 33/7) + 52/5 *sin(13*t + 5/3) + 343/18 *sin(14*t + 5/3) + 11/7 *sin(15*t + 2) + 19/6 *sin(16*t + 13/9) + 23/9 *sin(18*t + 7/4) + 175/22 *sin(19*t + 12/7) + 38/7 *sin(20*t + 8/5) + 4/3 *sin(21*t + 23/5) + 39/8 *sin(22*t + 13/8) + 2/5 *sin(23*t + 33/8) + 1/5 *sin(24*t + 5/7) - 965/2)*Heaviside(43*Pi - t)*Heaviside(t - 39*Pi) + (45 *sin(t + 41/9) + 13/9 *sin(2*t + 20/19) + 4066/5)*Heaviside(39*Pi - t)*Heaviside(t - 35*Pi) + (-26/9 *sin(1 - 2*t) - 307/5 *sin(5/4 - t) + 1475/3)*Heaviside(35*Pi - t)*Heaviside(t - 31*Pi) + (616/5 *sin(t + 9/2) + 5/7 *sin(2*t + 14/3) + 7504/5)*Heaviside(31*Pi - t)*Heaviside(t - 27*Pi) + (-325/6 *sin(3/2 - t) + 20/3 *sin(2*t + 18/5) + 17/3 *sin(3*t + 5/7) + 9325/9)*Heaviside(27*Pi - t)*Heaviside(t - 23*Pi) + (-7 *sin(3/4 - 3*t) - 558/7 *sin(9/7 - t) + 39/19 *sin(2*t + 2) + 7/4 *sin(4*t + 14/5) + 11717/18)*Heaviside(23*Pi - t)*Heaviside(t - 19*Pi) + (329/4 *sin(t + 21/5) + 13/6 *sin(2*t + 9/4) + 10651/15)*Heaviside(19*Pi - t)*Heaviside(t - 15*Pi) + (-26/3 *sin(2/7 - 2*t) - 989/7 *sin(4/3 - t) + 28/3 *sin(3*t + 6/5) + 3/4 *sin(4*t + 24/7) - 2177/5)*Heaviside(15*Pi - t)*Heaviside(t - 11*Pi) + (-15/7 *sin(1/2 - 54*t) - 29/8 *sin(1/6 - 52*t) - 35/6 *sin(14/9 - 45*t) - 5/4 *sin(15/16 - 43*t) - 69/8 *sin(1 - 39*t) - 23/5 *sin(13/12 - 37*t) - 29/6 *sin(10/11 - 34*t) - 117/5 *sin(10/7 - 30*t) - 222/13 *sin(13/9 - 25*t) - 67/2 *sin(17/11 - 22*t) - 146/3 *sin(5/4 - 18*t) - 268/5 *sin(6/11 - 14*t) - 337/12 *sin(4/3 - 10*t) - 131 *sin(5/6 - 8*t) + 2689/3 *sin(t + 3) + 235/8 *sin(2*t + 11/7) + 145/2 *sin(3*t + 1/5) + 552/5 *sin(4*t + 23/5) + 921/7 *sin(5*t + 5/6) + 220/7 *sin(6*t + 9/2) + 575/16 *sin(7*t + 38/37) + 1001/40 *sin(9*t + 7/9) + 342/7 *sin(11*t + 3/4) + 115/4 *sin(12*t + 23/5) + 43 *sin(13*t + 17/6) + 112/3 *sin(15*t + 17/5) + 799/19 *sin(16*t + 19/10) + 305/8 *sin(17*t + 23/7) + 286/7 *sin(19*t + 21/8) + 1513/28 *sin(20*t + 3) + 77/4 *sin(21*t + 17/4) + 301/15 *sin(23*t + 28/11) + 121/7 *sin(24*t + 7/4) + 66/7 *sin(26*t + 16/5) + 43/3 *sin(27*t + 18/5) + 35/4 *sin(28*t + 38/11) + 109/12 *sin(29*t + 23/8) + 39/7 *sin(31*t + 19/6) + 8 *sin(32*t + 16/5) + 7/4 *sin(33*t + 7/3) + 32/9 *sin(35*t + 19/5) + 3 *sin(36*t + 28/27) + 17/4 *sin(38*t + 9/5) + 29/6 *sin(40*t + 4/7) + 31/8 *sin(41*t + 19/6) + 38/7 *sin(42*t + 1/3) + 47/12 *sin(44*t + 5/3) + 26/9 *sin(46*t + 27/7) + 45/7 *sin(47*t + 13/10) + 23/12 *sin(48*t + 24/7) + 38/5 *sin(49*t + 22/7) + 19/5 *sin(50*t + 9/7) + 5/2 *sin(51*t + 31/7) + 36/7 *sin(53*t + 8/3) - 3366/5)*Heaviside(11*Pi - t)*Heaviside(t - 7*Pi) + (-4/5 *sin(4/5 - 21*t) - 8/5 *sin(1/4 - 20*t) - 2 *sin(5/4 - 15*t) + 1662/5 *sin(t + 34/9) + 197/5 *sin(2*t + 8/3) + 364/11 *sin(3*t + 3) + 212/3 *sin(4*t + 14/3) + 388/9 *sin(5*t + 2) + 43 *sin(6*t + 29/14) + 71/5 *sin(7*t + 1/4) + 165/7 *sin(8*t + 3/8) + 153/11 *sin(9*t + 25/6) + 94/9 *sin(10*t + 3/2) + 37/4 *sin(11*t + 32/11) + 30/7 *sin(12*t + 2/3) + 53/10 *sin(13*t + 41/9) + 9/5 *sin(14*t + 19/5) + 31/8 *sin(16*t + 10/7) + 13/4 *sin(17*t + 31/7) + 31/16 *sin(18*t + 4/7) + sin(19*t + 3/2) + 7/5 *sin(22*t + 23/8) - 5601/8)*Heaviside(7*Pi - t)*Heaviside(t - 3*Pi) + (-2/7 *sin(5/4 - 42*t) - 35/12 *sin(3/4 - 38*t) - 6/5 *sin(3/8 - 36*t) - 25/13 *sin(46/45 - 32*t) - 19/8 *sin(2/7 - 30*t) - 23/3 *sin(5/8 - 24*t) - 65/6 *sin(5/11 - 22*t) - 34/5 *sin(4/5 - 19*t) - 16 *sin(7/6 - 13*t) - 330/7 *sin(1/4 - 10*t) - 10765/7 *sin(1/8 - t) + 6479/18 *sin(2*t + 8/7) + 1300/7 *sin(3*t + 59/15) + 598/9 *sin(4*t + 17/8) + 413/4 *sin(5*t + 6/7) + 187/5 *sin(6*t + 14/3) + 534/11 *sin(7*t + 14/5) + 185/6 *sin(8*t + 13/7) + 371/9 *sin(9*t + 12/7) + 431/10 *sin(11*t + 23/5) + 121/7 *sin(12*t + 18/7) + 107/3 *sin(14*t + 14/5) + 174/5 *sin(15*t + 7/6) + 19/5 *sin(16*t + 41/9) + 160/11 *sin(17*t + 12/7) + 16/3 *sin(18*t + 4/3) + 45/4 *sin(20*t + 39/11) + 75/4 *sin(21*t + 6/5) + 34/33 *sin(23*t + 7/5) + 61/12 *sin(25*t + 40/9) + 39/5 *sin(26*t + 145/36) + 190/27 *sin(27*t + 21/8) + 2 *sin(28*t + 3/4) + 3/2 *sin(29*t + 8/7) + 8/5 *sin(31*t + 17/11) + 21/5 *sin(33*t + 5/2) + 38/7 *sin(34*t + 11/9) + 23/7 *sin(35*t + 1/4) + 24/7 *sin(37*t + 9/10) + 15/8 *sin(39*t + 13/4) + 13/5 *sin(40*t + 18/17) + 17/11 *sin(41*t + 2/5) + 23/11 *sin(43*t + 1/8) + 57/8)*Heaviside(3*Pi - t)*Heaviside(t + Pi))*Heaviside(sqrt(signum(sin(t/2))))

Denis

Senior Member
I memorized that in the 1970's....but "lost it"
shortly after, from a hockey stick on da noggin' Harry_the_cat

Senior Member
mmm4444bot, well I won't be typing that into my graphics calculator!

Jomo

Elite Member
I memorized that in the 1970's....but "lost it"
shortly after, from a hockey stick on da noggin' So that is what happened to you. Now I understand everything.

Denis

Senior Member
So that is what happened to you. Now I understand everything.
Well I have my hockey stick excuse...you have none!!

mmm4444bot

Super Moderator
Staff member
I memorized that in the 1970's … but "lost it" …
… I won't be typing that into my graphics calculator!
I'd thought interested folk would copy-n-paste to their favorite CAS. Now, I've realized that not all graphing software recognizes stuff like Heaviside() or signum() and there could be other issues with direct copying. Sorry 'bout that.

Here's the parametric plot, as produced using MVR5. Harry_the_cat

Senior Member
I'd thought interested folk would copy-n-paste to their favorite CAS. Now, I've realized that not all graphing software recognizes stuff like Heaviside() or signum() and there could be other issues with direct copying. Sorry 'bout that.

Here's the parametric plot, as produced using MVR5.

View attachment 11073
Wonderful! BTW what does Heaviside and signum do?

mmm4444bot

Super Moderator
Staff member
…what [do] Heaviside and signum do?
Heaviside is a step function; you can read about it at wikipedia. I learned its use only as it's applied in Laplace transforms (i.e., solving differential equations). I just learned that multiple Heaviside versions exist.

$$\displaystyle H(n) = \begin{cases} 0, \; n < 0 \\ 1, \; n \ge 0 \end{cases}$$

Signum is a function that returns the sign of its argument. It also has an entry at wikipedia.

$$\displaystyle signum(x) = \begin{cases} -1, \; x < 0 \\ \;\; 0, \; x = 0 \\ \;\; 1, \; x > 0 \end{cases}$$

For non-zero inputs, I've also seen signum defined as x/|x|.

Subhotosh Khan

Super Moderator
Staff member
Heaviside is a step function; you can read about it at wikipedia. I learned its use only as it's applied in Laplace transforms (i.e., solving differential equations). I just learned that multiple Heaviside versions exist.

$$\displaystyle H(n) = \begin{cases} 0, \; n < 0 \\ 1, \; n \ge 0 \end{cases}$$

Signum is a function that returns the sign of its argument. It also has an entry at wikipedia.

$$\displaystyle signum(x) = \begin{cases} -1, \; x < 0 \\ \;\; 0, \; x = 0 \\ \;\; 1, \; x > 0 \end{cases}$$

For non-zero inputs, I've also seen signum defined as x/|x|.
Heaviside - an electrical engineer - used Heaviside's operational methods of electric circuit analysis, where Laplace transform was used "intuitively". It is said that Heaviside was asked to "prove" that his method, he reportedly said that "It works". Later somebody else discovered that Laplace had formalised the method ~100 years before him.

Harry_the_cat

Senior Member
Thanks mmm and Subho.

mmm4444bot

Super Moderator
Staff member
… Heaviside was asked to "prove" [his] method, he reportedly said that "It works" …
Gotta love those engineer and physicist types! They get my Valentines. :cool: