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

**Circle Rolling around Rolling Circle (1)**

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

Circle 2 rolls around **inside** of Circle 1.

**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.

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

My Gallery of Math Art: benice equation

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi benice;

Nice work!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

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

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.

My Gallery of Math Art: benice equation

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

hi benice

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

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

**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

**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.

My Gallery of Math Art: benice equation

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi benice;

Looks like a fish!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

My Gallery of Math Art: benice equation

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi benice;

That is very well done. Thanks!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

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."

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

gAr wrote:

Hi benice,

That's very cool!

cool it looks good and spirography

Hey.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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

i have geogebra but how do you make that?

Hey.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

What do you know how to do with geogebra?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

mathgogocart wrote:

i have geogebra but how do you make that?

My Gallery of Math Art: benice equation

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