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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


Curves of mathematical gymkhana 2012-2013  

Project made by the students of Bachelor's Degree in Telecomunications Systems, Sound and Image Engineering. Gandia Campus Site. Universitat...

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