How can I get a curve from a trace, and calculate it's length?

Nicholasfox shared this question 6 months ago
Answered

As follow:

https://www.geogebra.org/cl...

I want to know the length of the trace of point P. Can I get a curve from a trace, or there's a direct way to calculate it's length?

Thanks.

Best Answer
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What you see in the algebra view is not exact the definition of the object.

You can see the definition for example in the Properties/Basic/Definition.

In the attachment it has some explanations. If not clear then please ask more specifically.

Comments (9)

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1

Bonjour ,

ça ressemble à une fonction sinus mais il faudrait savoir comment est défini le point P

Cordialement

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2

If we think a little bit more direct to reduce dependencies to one variable t (k),

we get a term of the moving point P and do integrate to the arc length

https://www.geogebra.org/m/qbfqhvyq

this is called Zykloide - Rollkurve

https://www.geogebra.org/m/dz28hcyy

there exist a command Locus( <Point Creating Locus Line>, <Slider> )and LocusEquation( <Locus> )

but I was not very successful with it...

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1

It is instructive,Thanks!

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2

With the parameter equation for cycloids (wikipedia) and with Locus()

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1

Amazing, I need some time to figure it out.Thank you, very much.

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2

Advanced: more general parameter equation for a and a' and more independent.

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1

Hi, how comes this Expression? I really can't understand.

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2

What you see in the algebra view is not exact the definition of the object.

You can see the definition for example in the Properties/Basic/Definition.

In the attachment it has some explanations. If not clear then please ask more specifically.

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1

I knew the basic usage of ggb, I just don't know the concept of the Cycloid/Trochoid/.

Your help was very much appreciated!

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