Curves of mathematical gymkhana 2012-2013

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Grado de Ingeniería de Sistemas de Telecomunicación, Sonido e Imagen Matemáticas 2 2012-2013 Curvas de la yincana matemática Bachelor's Degree in Telecommunications Systems, Sound and Image Engineering Mathematics 2 2012-2013 Curves of mathematical gymkhana

Curvas generadas con MatlabŠ

Curves generated with MatlabŠ

Curvas en forma paramĂŠtrica Curves in parametric form

Hipotrocoides Hipocicloides Epitrocoides Epicicloides

Hypotrochoids Hypocycloids Epitrochoids Epicycloids

Hipocicloide- Hypocycloid A=8

B=7

Autores-Authors: Francisco Boix – Jorge Nieto

Hipotrocoide-Hypotrochoid 5 4

x=(0.4)cos(t)+5.2cos((2/13)t) y=(0.4)sin(t)-5.2sin((2/13)t)

3 2 1 0 -1 -2 -3 -4 -5 -6

-4

-2

Autores-Authors: Adriana Soler – Marina Ballester

0

2

4

6

Hipotrocoide-Hypotrochoid

x=6.5cos(t)+4cos(2.6t) y=6.5sin(t)+4sin(2.6t)

Autores-Authors: Dídac Diego i Tortosa - Carles Fèlix Tur

Hipotrocoide-Hypotrochoid

x=6.9cos(t)+5cos(1.15t) y=6.9sin(t)-5sin(1.15t)

Autores-Authors: Diego Rausell – Ferran Ulldemolins

10 8 6 4

x=8.3cos(t)-1.5cos((8.3/0.6)t) y=8.3sin(t)-1.5sin((8.3/0.6)t)

2 0 -2 -4 -6 -8 -10 -10

-8

-6

-4

Autores-Authors: Juan Gonzalez - Victor Llinares

-2

0

2

4

6

8

10

Hipotrocoide-Hypotrochoid

x=8.9cos(t)+0.4cos((8.9/1.1)t) y=8.9 sin(t)-0.4sin((8.9/1.1)t)

Autores-Authors: Adrián Blay Lorente - Rubén Rodríguez Tur

Hipotrocoide-Hypotrochoid

x=(6.4-2)cos(t)+2cos((6.4-2/2)t) y=(6.4-2)sin(t)+2sin((6.4-2/2)t)

Autores-Authors: Vicent Avaria Avaria, Josep Andreu CerdĂ

Hipotrocoide-Hypotrochoid

x=8cos(t)+5cos(4t) y=8sin(t)-5*sin(4t) 8.9

Autores-Authors: Alberto Aguilar Narbona – Pablo Gómez Magenti

Epitrocoide-Epitrochoid 10 8 6 4

X=-2.3cos(t)+6cos(-0.8t) Y=-2.3sin(t)+6sin(-0.8t)

2 0 -2 -4 -6 -8 -10 -10

-8

-6

-4

-2

0

Autores-Authors : Rafa Bono Aguilar - David Carrasco Peris

2

4

6

8

10

Epicicloide-Epicycloid

x=27cos(t)-3cos(9t) y=27sin(t)-3sin(9t)

Autores-Authors: Anna Vidal - Bernardino Roig

Otras curvas planas en forma paramĂŠtrica Other planar curves in parametric form

Rosa de 16 pĂŠtalos- Rose with 16 petals

x=sin(8t/5)cos(t) y=sin(8t/5)sin(t)

Autores-Authors: Alejandro Juan- Joseba Elcano

Curva de Lissajous-Lissajous curve

x=sin(t); y=sin(2t);

Autores-Authors: Lamberto Sรกnchez - Pablo Hernรกndez

Astroide-Astroid

x=cos3(t) y=sin3(t)

Autores-Authors: Deyvid Grishev - Adriana Florea

x=t+2sin2t y=t+2cos5t

Autores-Authors: Àngela Molina Sancho – María Puentes Margarito

Curva escurridiza-Slippery curve 15

10

x = a cos t – b cos pt y = csin(t) – dsin(qt)

a = 16, b = 5, c = 12, d = 3, p = 47/3 , q = 44/3

5

0

-5

-10

-15 -40

-30

-20

-10

0

Autores-Authors: Marcos Guerra Vega - Arturo León Cabello

10

20

30

40

x=cos(t)-cos(80t)sin(t) y=2sin(t)-sin(80t)

Autores-Authors: Alejandro Juan- Joseba Elcano

Curvas en el espacio, forma paramÊtrica Curves in space, paramètric form

Nudo de trébol-Trefoil knot

x=(2+cos(1.5t))cos(t) y=(2+cos(1.5t))sin(t) z=sin(1.5t)

Autores-Authors: Rubén Martínez - Josep Rioja

Espiral Toroidal-Toroidal spiral

x= (4+sin20t)cos t y= (4+sin20t)sin t z= cos 20t

Autores-Authors: José Luis Campello – David Hernández

x=cost y=sint z=sin5t

Autores-Authors: I単aki Abrego . Juanjo silgo

Muelle Slinky-Slinky Spring 1.5 1

x=(1+0.4cos(31.5t))cos(t) y=(1+0.4cos(31.5t))sin(t) z= 0.3t+0.4sin(31.5t)

0.5 0 -0.5 -1 -1.5 2 1

2 1

0

0

-1

-1 -2

Autores-Authors: Ram贸n Rodr铆guez- Gabriel Oltra

-2

H茅lice cil铆ndrica-Cylindrical helix

x=3cos(2t) y=3sin(2t) z=8t

Autores-Authors: Eva Zan贸n - Alfredo Gasc贸n

Curvas en forma polar Curves in polar form

Rosas Roses

Rosa de tres petalos- Rose with three petals

r = 3cos(3t)

Autores-Authors: ร scar Peirรณ - Adriรกn Gonzรกlez

Rosa de quatre pètals- Rose with four petals

r=2sin(2t)

Autores-Authors: Dídac Diego i Tortosa - Carles Fèlix Tur

90

1

120

60 0.8 0.6

150

r=cos(2t)

30 0.4 0.2

180

0

210

330

240

300 270

Autores-Authors: Juan Gonzalez - Victor Llinares

Rosa de quatre pètals- Rose with four petals 90

2

120

60 1.5

r=2cos2t

1

150

30

0.5

180

0

210

330

240

300 270

Autores-Authors: Valko Lachezarov Valkov- Andreu Garcia Serra

Rosa de 5 pĂŠtalos- Rose with five petals 90

1 60

120 0.8

0.6 30

150

r = sin(5t)

0.4

0.2

180

0

210

330

240

300

270

Autores-Authors: Adriana Soler – Marina Ballester

Rosa de 5 pĂŠtalos- Rose with five petals

r = 2sin(5t)

Autores-Authors: Alejandro Lopez Lopez – David Tamarit Belenguer

r=2cos(5t)

Autores-Authors: Luis Núñez Rodríguez - Manuel Jesús Parrilla Navarro

Rosa de 8 pétals- Rose with 8 petals 90

2

120

60 1.5 1

150

r = 2cos(4t)

30

0.5

180

0

210

330

240

300 270

Autores-Authors: Ramón Rodríguez- Gabriel Oltra

90 2 120

60

1.5

150

30

1

r=2cos(3t/2) 0.5

180

0

210

330

240

300

270

Autores-Authors: Rafa Bono Aguilar - David Carrasco Peris

Rosa de 16 pétals - Rose with 16 petals 90

1

120

60 0.8

r = sin(8t/5)

0.6 150

30 0.4 0.2

180

0

330

210

300

240 270

Autores-Authors: Ramón Rodríguez- Gabriel Oltra

90 2 60

120

1.5

150

30

1

r=2cos(3t/2)

0.5

180

0

210

330

240

300

270

Autores-Authors: Pablo Esparza - Rubén Sáez

Rosa de 17 pétalos - Rose with 17 petals

r=sin(8t/5)

Autores-Authors: Rubén Martínez - Josep Rioja

r=sin(9t/4)

Autores-Authors: Eva Zan贸n - Alfredo Gasc贸n

r=3+2sin (6t)

Autores-Authors: Laura Mainar- Clara Luz贸n

r=2+cos(6t)

Autores-Authors: Dídac Diego i Tortosa - Carles Fèlix Tur

Mariposas Butterflies

Autores-Authors: Francisco Boix – Jorge Nieto

r=exp(sint) -2cos(4t)

Autores-Authors: Vicent Avaria Avaria, Josep Andreu CerdĂ

Cardioides, caracoles, nautilus, … Cardioid, Limaçons, nautilus, …

Cardioide - Cardioid

r=1-cos(t);

Autores-Authors: Lamberto Sรกnchez - Pablo Hernรกndez

Nefroide de Freeth - Nephroid of Freeth

r = 1+2sin(t/2)

Autores-Authors: Alejandro Lopez Lopez – David Tamarit Belenguer

r=2-5cos(t)

Autores-Authors: Diego Rausell – Ferran Ulldemolins

90

5

120

60 4 3

150

r=2+cos(3t)

30 2 1

180

0

210

330

240

300 270

Autores-Authors: Juan Gonzalez - Victor Llinares

Nefroide de Freeth - Nephroid of Freeth

r= 1 + 2 sin (t/2)

Autores-Authors: Adrián Blay Lorente - Rubén Rodríguez Tur

Nautilus

r= ½ + sin(t)

Autores-Authors: Germán Egea Almela - Alejandro López San Martín

Caracol - Limaçon

r=(1/2)+cos(t)

Autores-Authors: Alberto Aguilar Narbona – Pablo Gómez Magenti

Caracol - Limaçon

c=-2 r=1+csin(t)

Autores-Authors: Rubén Martínez - Josep Rioja

90

6

120

60 4

150

r=2+4cos2t

30 2

180

0

210

330

240

300 270

Autores-Authors: Valko Lachezarov Valkov- Andreu Garcia Serra

Nautilus

r =(3/2)-sint

Autores-Authors: ร scar Peirรณ - Adriรกn Gonzรกlez

Nautilus

r = 2 + cos(t)

Autores-Authors: Germán Egea Almela – Alejandro López San Martín

90

Nautilus

3 60

120 2

30

150 1

r = -2 + sin(t) 180

0

210

330

240

300 270

Autores-Authors: Marcos Guerra Vega - Arturo Le贸n Cabello

Otras curvas en coordenadas polares Other curves in polar coordinates

Espiral - Spiral

r=3t

Autores-Authors: Lamberto Sรกnchez - Pablo Hernรกndez

r=(1+sin(t))cos(2t)

Autores-Authors: Diego Rausell – Ferran Ulldemolins

r=1+4cos(5t)

Autores-Authors: Laura Mainar- Clara Luz贸n

Gracias a los alumnos del primer curso del Grado de Ingeniería de Sistemas de Telecomunicación, Sonido e Imagen Campus de Gandia Universitat Politècnica de València

Thanks to the students of the first year of the Bachelor's Degree in Telecommunications Systems, Sound and Image Engineering Gandia Campus Site Universitat Politècnica de València

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