iterate squares and arcs

lawrence shared this question 3 years ago
Answered

Need to know how to draw a fibonacci spiral using custom tool and iteration/sequence command to draw the series of squares and arcs for each value of n. later find sum of the series .Any help or advise is much appreciated. Thanks

Comments (6)

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hello

you can do the custom tool yourself


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


if you need I can do it

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Thanks very much. I managed creating the square and arc custom tools but need help as to how to use iteration and sequence commands to draw the fibonacci spiral without the need to do it manually. Any help will be much appreciated. Thanks

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Hi lawrence!

Hmm, sorry for answering, I am pretty sure, that mathmagic will do it later with a much more competent advice.

I see your file, but that's "so manually" for a special case and, sorry to say that, but there is no "system" or "concept".

As a constructive hint - take a look at your posted picture and look at the black arcs.

They are all quadrants with the radius of a fibonacci-number.

To paint these quadrants, you only need three points to use the CircularArc-Command (midpoint, starting point, ending point)


In the same way you need only two points to use the Polygon-Command to get the quadrats.

So it is much easier, and I also think better, to think about how you can get these needed points and it is not necessary, to construct them in a way, you probably think first.

You can start at a point, I think (0,0) is a good starting point. ;-)

And now you can "see", that you always walk in a specific direction and a specific distance to get your next needed point and from these next point you get your next point always by turning 90° and a new specific distance, which, obviously have something to do with a fibonacci-number. ;-)

And not all corner-points of the quadrats are needed to construct the quadrats.


So you need the fibonacci-numbers, a starting point and a way to come to the next needed points and a number n that counts the fibonacci-number.

I am pretty sure, that this can be done in a spreadsheet, but I've done it in Algebra with the Binet Formula, because you speaked of sequence-commands in your first post.

So sorry for interfering but I hope, it helps a little bit.


Kind Regards

mire2

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you can create all arcs and squares you need (dragging the rows of spreadsheet down) and show only the account you need to show in graphics with a slider

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Hi lawrence!

One possibility is to use Binet's Formula: https://en.wikipedia.org/wi...

You can use it e. g. in CAS in numerical modus, so you get the Fibonacci-Numbers in a directly and not in a recursive form.

That makes it quite easier to define the squares and arcs in a sequence command.

I think, you can manage it now.

Kind Regards

mire2

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if you want to use the Binet formula the tool is easier because you need less poinst in sucesive steps because An+1/An is known

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