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For example, I want to plot a circle with a polar equation:

How would I do such a thing?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

Geogebra uses the Curve command for that.

1)Enter in the input box:

c = Curve[2 cos(t), 2 sin(t), t, 0, 2 pi]. You will see a circle with r = 2.

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**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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What is the syntax of the curve command exactly like?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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The syntax is as I posted it.

c = Curve[2 cos(t), 2 sin(t), t, 0, 2 pi]. This is straight from the polar coordinate equation of a circle. This one has a radius of 2. Try it.

Want to see a few more curves?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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Yes! with pleasure

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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This is a cardioid.

Curve[5 (1 + 2cos(t) + cos(2t)), 5 (2sin(t) + sin(2t)), t, 0, 6.28319]

See the first picture.

For a cycloid:

Curve[5 (t - sin(t)), 5 (1 - cos(t)), t, 0, 25.13274]

see the second picture.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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Will you please explain the nature of the curve statement?

I do not understand it at all

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

It uses a variable called t to generate the x and y coordinates.

Curve[2 cos(t), 2 sin(t), t, 0, 2 pi]

t goes from 0 to 2 pi. That is what t,0, 2pi is for. x = 2 cos(t) and y = 2 sin(t) are the first two values in the curve command.

You could manually follow this with a table of values:

t

------------------------------------------

2 cos(t)

-------------------------------------------

2 sin(t)

Have you ever done that with a parametric equation?

Programming and especially geogebra are a hands on thing. Please do the examples in geogebra.

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Well cant we specify an equation in the form:

?

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'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

Not at present. We can view the graph in polar coordinates but not graph it directly. To get around this we use the parametric equations that represent the equation.

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Let me google parametric equations

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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Hmm I googled it and found that the curve command draws a parametric curve only

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

Yes, but a polar equation can be expressed in terms of a parametric one. Then you can use Curve.

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Are your enemies "ridiculous" and are you "stupid" enough?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

Are your enemies "ridiculous"

Yes! They are almost as ridiculous as I am. If they work at it they may catch up, who knows. The quote is by Voltaire and almost anyone is ridiculous compared to him. I just liked the quote.

I believe that I am stupid enough but not polite enough.

Happy Birthday!

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Thanks but it is not yet 29th in our country.

The time now here is August 28, 5:44 PM

I believe that I am stupid enough but not polite enough.

But I think you are polite enough and not so stupid yet

Your enemies are ridiculous

I hope it doesn't mean that anyone who is ridiculous are your enemies!

Would you please see my question on the other Thread titled "Pi"? Should I have submitted it under "Computer Math"?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

Okay, sorry for the incorrect date. I will get you tomorrow,

and not so stupid yet

Of all the faults a man can have they say pride is the worst but the worst one is laziness. If a person works hard and is stupid they can sometimes pass up someone who is lazy and brilliant. Speaking of myself I have worked very hard at mathematics but now have more to learn then when I started. In that sense I am stupid. The more you know, the more you know that you do not know.

I had to learn politeness. I come from a rude country, a rude city and a heritage of rude people. In other words from the gutter, the ghetto, the slum...

Your problem is posted in the correct section. I have looked at it but I am sorry that I can not yet assist you with it. Nothing is coming to me to post.

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But all I want is to know how the algorithm works. That one is really great. It continuously outputs the digits of the Pi forever.

An other way of calculating the digits of Pi is the AM-GM method.

But my program runs out of decimal Precision too quick

By The Way, I know it is stupid but I have learnt Pi upto 20 digits

3.14159265358979323846....

Not only stupid but also useless

*Last edited by Agnishom (2012-08-28 01:45:44)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

It is not stupid or useless. For me it was the zeta functions.

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How is it useful???????????

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

How is it useful???????????

Like all mental gymnastics it increases your mental power. It is just like lifting weights. Of what use is pushing that iron? There is no use in moving barbells around other than to increase your physical strength and stamina. Using your brain while young is exactly the same thing.

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How do I convert Polar equation into paramtric ones?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Hi Agnishom;

You use the two equations

and substitute for r.

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In every case?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

Yes, I believe so.

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