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#1 2011-12-08 22:49:33

benice
Member
Registered: 2010-06-10
Posts: 110

[Dynamic Spirograph] Circle Rolling around Rolling Circle

Circle Rolling around Rolling Circle (1)

Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.

hypo_hypotrochoid_001.gif


Circle Rolling around Rolling Circle (2)

Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.


Circle Rolling around Rolling Circle (3)

Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.


Circle Rolling around Rolling Circle (4)

Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.


Sumo Wrestler

Insect-like Spirograph

Making Love (♥)

Spiroface

Last edited by benice (2012-05-02 04:29:03)


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#2 2011-12-09 00:45:12

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi benice,

That's extraordinary!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#3 2011-12-09 04:46:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi benice;

Nice work!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#4 2011-12-15 08:37:46

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Can you do the logarhythm of the distances to make it possible to see this one:
Make the big moving circle go around the sun, like Earth.  And then make the tiniest circle go around the Earth like the moon.
Don't use logs at first but one is 94 million miles and the other one is a quarter of a million, or something like that so it might not be easy to view it since 4 times 94+/- is around 376 for the ratio of the earth and moon circle sizes.  Now looking down at the solar system from the north star, the Earth goes CCW and the moon also goes CCW, the last time I remember.`


igloo myrtilles fourmis

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#5 2012-01-09 12:29:58

benice
Member
Registered: 2010-06-10
Posts: 110

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

John E. Franklin wrote:

Can you do the logarhythm of the distances to make it possible to see this one:
Make the big moving circle go around the sun, like Earth.  And then make the tiniest circle go around the Earth like the moon.
Don't use logs at first but one is 94 million miles and the other one is a quarter of a million, or something like that so it might not be easy to view it since 4 times 94+/- is around 376 for the ratio of the earth and moon circle sizes.  Now looking down at the solar system from the north star, the Earth goes CCW and the moon also goes CCW, the last time I remember.`

Hi John,

Please see the attached image sun_earth_moon_d2_0.png for the orbit of the moon around the sun.

The parameter values I use:
The radius of the Sun = 69.55 × 10^4 km.
The radius of the Earth = 0.6371 × 10^4 km.
The radius of the Moon = 0.17371 × 10^4 km.
The average distance from the Earth to the Sun = 14959.787 × 10^4 km.
The average distance from the Moon to the Earth = 38.5 × 10^4 km.
The period of the Earth's orbit around the Sun = 365.2422 days.
The period of the Moon's orbit around the Earth = 27.32 days.
Earth's rotation period = 1 day.
Moon's rotation period = 27.32 days.

Suppose P2 is a point which is (d2 × 10^4 km) away from the center of the Moon
and is fixed relative to the Moon.
Please see images sun_earth_moon_d2_200.jpg ~ sun_earth_moon_d2_4000.jpg
for the orbits of P2 around the sun with some different d2 values.

Suppose P1 is a point which is (d1 × 10^4 km) away from the center of the Earth
and is fixed relative to the Earth. P is the midpoint between P1 and P2.
Please see the following images for the orbits of P around the sun with some d1 and d2 values:
sun_earth_moon_d1_3000_d2_5000.jpg,
sun_earth_moon_d1_5000_d2_1000.jpg,
sun_earth_moon_d1_5000_d2_3000.jpg.

View Image: sun_earth_moon_d1_3000_d2_5000.jpg View Image: sun_earth_moon_d1_5000_d2_1000.jpg View Image: sun_earth_moon_d1_5000_d2_3000.jpg View Image: sun_earth_moon_d2_0.png View Image: sun_earth_moon_d2_1000.jpg View Image: sun_earth_moon_d2_200.jpg View Image: sun_earth_moon_d2_2000.jpg View Image: sun_earth_moon_d2_4000.jpg View Image: sun_earth_moon_d2_500.jpg

My Gallery of Math Art: benice equation

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#6 2012-01-09 12:41:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

hi benice

this pics are very nice.keep doing what you're doing cuz you're doing it awsome...ly. up

Last edited by anonimnystefy (2012-01-09 12:41:35)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2012-01-09 12:42:12

benice
Member
Registered: 2010-06-10
Posts: 110

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Circle Rolling around Rolling Circle (2)

Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.


My Gallery of Math Art: benice equation

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#8 2012-01-09 12:46:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi;

Your stuff looks a lot better than many of the geogebra tutorials I have seen. A step by step on some of them would be an education.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2012-01-09 13:06:46

benice
Member
Registered: 2010-06-10
Posts: 110

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi anonimnystefy,

Thank you for your appreciation.



Hi bobbym,

There are some new features in GeoGebra 4.0.


My Gallery of Math Art: benice equation

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#10 2012-01-09 13:15:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi benice;

Yes, I know I keep abreast of the program. Have not seen the 3D version as a standalone download yet.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2012-01-27 07:19:12

benice
Member
Registered: 2010-06-10
Posts: 110

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Circle Rolling around Rolling Circle (3)

Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.


Circle Rolling around Rolling Circle (4)

Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.


Sumo Wrestler


Insect-like Spirograph


My Gallery of Math Art: benice equation

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#12 2012-01-27 08:06:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi benice;

Looks like a fish!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2012-02-08 15:00:20

benice
Member
Registered: 2010-06-10
Posts: 110

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle


My Gallery of Math Art: benice equation

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#14 2012-02-08 17:27:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi benice;

That is very well done. Thanks!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#15 2012-02-08 18:53:51

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi benice,

That's very cool!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Online

#16 2012-04-29 02:21:25

mathgogocart
Member
Registered: 2012-04-29
Posts: 1,426

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

gAr wrote:

Hi benice,

That's very cool!

cool it looks good and spirographyupup


Hey.

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#17 2012-04-29 02:26:03

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

Hi

Yes,benice does know how to creaty soke very awesome pics.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#18 2012-05-14 10:55:53

mathgogocart
Member
Registered: 2012-04-29
Posts: 1,426

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

i have geogebra but how do you make that?


Hey.

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#19 2012-05-14 11:02:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,032

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

What do you know how to do with geogebra?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#20 2012-05-16 20:36:18

benice
Member
Registered: 2010-06-10
Posts: 110

Re: [Dynamic Spirograph] Circle Rolling around Rolling Circle

mathgogocart wrote:

i have geogebra but how do you make that?

Here is an example.


My Gallery of Math Art: benice equation

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