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1 Attachment(s)
Double the Area of a Circle
Using any Xara tools, can you create a circle and without any calculations render another circle to be double the original circle's area?
Attachment 122519
Acorn
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2 Attachment(s)
Re: Double the Area of a Circle
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Re: Double the Area of a Circle
Quote:
Originally Posted by
gwpriester
Two ways.
Gary, I think you have increased the area fourfold.
It is not clear when and why I would stop dragging.
Acorn
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Re: Double the Area of a Circle
ah now... scaling width to 200% fixed aspect is going to give a circle a lot bigger than just double the surface area [4 times ? ] - scaling it by 200% in just one aspect might produce an object twice the surface area.. but not of course a circle, an elipse
simply dragging out the circle may not work either without some sort of calculation so you know when to stop...
gonna need to think about this if we are not allowed to enter actual measurements...
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Re: Double the Area of a Circle
cross posted with acorn :)
I had this argument 20 years ago about whether 50% of A3 is A4 or A5 - depends of course whether you mean by surface area or by fixed aspect... sadly the photocopier got it the wrong way round to what was required
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
ah now... scaling width to 200% fixed aspect is going to give a circle a lot bigger than just double the surface area [4 times ? ] - scaling it by 200% in just one aspect might produce an object twice the surface area.. but not of course a circle, an elipse
simply dragging out the circle may not work either without some sort of calculation so you know when to stop...
gonna need to think about this if we are not allowed to enter actual measurements...
Yep, doubling both X- & Y-dimensions makes the area four times bigger!
Acorn
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Re: Double the Area of a Circle
Hi Acorn,
Select a circle and scale it up by 141.4142% - Change it's width by 141.4142% or if you have lock aspect ratio off, then change both it's width and height by 141.4142%.
Many thanks,
Ben
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Re: Double the Area of a Circle
well having though you need to increase the circle by 133.3333333[ad naus.] % in fixed aspect - not too helpful in a decimal calculation if you want precision, but a step in the right direction maybe
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
cross posted with acorn :)
I had this argument 20 years ago about whether 50% of A3 is A4 or A5 - depends of course whether you mean by surface area or by fixed aspect... sadly the photocopier got it the wrong way round to what was required
As two sheets of A5 is one A4 and two of A4 is one A3, I would have argued it was 50% area. To get there you need to scale dimensions 70.71% [(√2)/2].
Acorn
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Re: Double the Area of a Circle
Quote:
Originally Posted by
Ben.Moses
Hi Acorn,
Select a circle and scale it up by 141.4142% - Change it's width by 141.4142% or if you have lock aspect ratio off, then change both it's width and height by 141.4142%.
Many thanks, Ben
No calculations Ben. Also not everyone easily remembers √2 as I am afraid you have shown. The correct scaling is 141.4213%.
Acorn
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Re: Double the Area of a Circle
Hi Acorn,
Did 141.4142% or 141.4213% not work for you?
Many thanks,
Ben
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Re: Double the Area of a Circle
cross posted with ben...
that rings a bell actually back to A sized paper in fact, the ratio of one side [eg 420mm] to the other [eg 594mm]
looking again I can see the 1.333 is obviously wrong... but still its an approximation to four decimal places
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
well having though you need to increase the circle by 133.3333333[ad naus.] % in fixed aspect - not too helpful in a decimal calculation if you want precision, but a step in the right direction maybe
Sorry but that increases the area to 177.7(r)%. We need 200%.
Again, don't calculate!
Acorn
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Re: Double the Area of a Circle
square root of 2 sounds like maths, not my subject 2 pi r squared and all that...
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Re: Double the Area of a Circle
yes I was looking at the wrong ratio.. so even a precentage is not allowed.... ok....
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
cross posted with ben...
that rings a bell actually back to A sized paper in fact, the ratio of one side [eg 420mm] to the other [eg 594mm]
looking again I can see the 1.333 is obviously wrong... but still its an approximation to four decimal places
For two A4s to have the area of one A3 and keep the sides in the same ration then the sides have to be ratio √2:1.
A4 is 297 x 210 mm and 297/210 is 1.414286 (594/420 clearly has the same ratio).
Acorn
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Re: Double the Area of a Circle
Quote:
Originally Posted by
Acorn
As two sheets of A5 is one A4 and two of A4 is one A3, I would have argued it was 50% area. To get there you need to scale dimensions 70.71% [(√2)/2].
Acorn
70.71% being the obverse [if thats the right word] of 141.4142
but this does not help with the problem <sigh>
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Re: Double the Area of a Circle
Quote:
Originally Posted by
Ben.Moses
Hi Acorn,
Did 141.4142% or 141.4213% not work for you?
Many thanks, Ben
Yes Ben, it did, but calculations are excluded in this Challenge.
Acorn
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
70.71% being the obverse [if thats the right word] of 141.4142
but this does not help with the problem <sigh>
'fraid so. 0.7071 is the inverse of 1.41421.
Acorn
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Re: Double the Area of a Circle
Hi Acorn,
My bad, thought you were asking for help, didn't realise this was a challenge.
Many thanks,
Ben
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Re: Double the Area of a Circle
Quote:
Originally Posted by
Ben.Moses
Hi Acorn, My bad, thought you were asking for help, didn't realise this was a challenge.
Many thanks, Ben
No worries Ben, some math / maths en route is no bad thing.
Acorn
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Re: Double the Area of a Circle
forgotten most of mine :o
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1 Attachment(s)
Re: Double the Area of a Circle
Trying to work from memory here, and you know how dangerous that is ...
Attachment 122525
Draw circle - rotate 45° - convert to editable shapes - break at points. Draw square - align to broken shapes - draw circle - stretch to align with edges of square.
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Re: Double the Area of a Circle
okay a simlpe solution - no calculation just an assumption:
make a circle 210mm wide this is your start point
align it to the bottom and sides of your page
drag it to increase size until it snaps to top of page - job done
given the assumption: your default page is A4 portrait no shadow
I guess this may be considered out-of-the-box if not disqualified in some way... but at least it follows on from what we have been saying, to which there was some point ;) :)
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1 Attachment(s)
Re: Double the Area of a Circle
I think you are onto something there keith..
how about:
make square same width/height as circle - the circle that aligns with the four corners of this square will be the one you want:
Attachment 122526
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Re: Double the Area of a Circle
Clue ... Sin 45 = O/H = 0.7071 ...
Therefore radius of inner circle = 0.7071 of radius of outer circle.
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Re: Double the Area of a Circle
oh please I knoweth not the math and the signs he giveth :)
edit - and besides, that's a calculation and therefore going off at a tangent [but I do see what you mean, I think - we have the same square root of 2 ratio, inverted, that acorn was refering to... ? I can handle ratios; but numbers, like letters, are apt to confuse me when they get serious as someone once said ]
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Re: Double the Area of a Circle
Quote:
Originally Posted by
ss-kalm
Trying to work from memory here, and you know how dangerous that is ...
Attachment 122525
Draw circle - rotate 45° - convert to editable shapes - break at points. Draw square - align to broken shapes - draw circle - stretch to align with edges of square.
Keith, good memory.
The length of the centre of the square to a corner is √2, which must therefore be the radius of the outer circle.
Your steps are more than I would have considered but it is a working solution.
Acorn
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
okay a simlpe solution - no calculation just an assumption:
make a circle 210mm wide this is your start point
align it to the bottom and sides of your page
drag it to increase size until it snaps to top of page - job done
given the assumption: your default page is A4 portrait no shadow
I guess this may be considered out-of-the-box if not disqualified in some way... but at least it follows on from what we have been saying, to which there was some point ;) :)
handrawn, it works so it is a solution.
Thereafter you could scale both circles at the same time to any other size.
In XWD(P), you don't have an A4 template so you would have to know the Custom dimensions to enter, but as there were no "calculations" you get a pass.
Acorn
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
I think you are onto something there keith..
how about
:
make square same width/height as circle - the circle that aligns with the four corners of this square will be the one you want:
Attachment 122526
That is a good refinement of Keith's approach.
i have a wheeze / trick / gimmick that I think improves even on this.
Acorn
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Re: Double the Area of a Circle
Quote:
...but as there were no "calculations" you get a pass.
:)
Quote:
That is a good refinement of Keith's approach
Keith's memory deserves the all the credit - I just looked at what he said and thought [like you] thats more complicated than it need be; I took the maths on trust
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Re: Double the Area of a Circle
Quote:
Originally Posted by
Acorn
i have a wheeze / trick / gimmick that I think improves even on this.
Acorn
well I guess if you have the starting circle aligned to the square all you have to do it drag it, or a clone, out to the corners - could it be much simpler than that?
or are we talking about a different approach ?
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1 Attachment(s)
Re: Double the Area of a Circle
Much simpler ... Show grid ... Snap to grid.
Attachment 122531
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Re: Double the Area of a Circle
Quote:
Originally Posted by
handrawn
oh please I knoweth not the math and the signs he giveth :)
edit - and besides, that's a calculation and therefore going off at a tangent [but I do see what you mean, I think - we have the same square root of 2 ratio, inverted, that acorn was refering to... ? I can handle ratios; but numbers, like letters, are apt to confuse me when they get serious as someone once said ]
I wasn't doing the actual calculation, just hinting at the solution.
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Re: Double the Area of a Circle
twas a good hint :) I just don't like maths
with regard to the snap points - how are you defining which ones to use?
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1 Attachment(s)
Re: Double the Area of a Circle
Quote:
Originally Posted by
ss-kalm
Keith, obviously stimulating the creative juices.
Without a grid, using Snap to Shapes:
Attachment 122532
Acorn
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Re: Double the Area of a Circle
ah another way of looking at the symmetry ;)
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1 Attachment(s)
Re: Double the Area of a Circle
My approach was to clone the circle and with the QuickShape tool change the clone to a square (create polygons, 4 sides).
Shift-dag a corner until the square is the same width/height as the original circle.
Final QuickShape tool change square back to a circle (Create ellipses).
My method clones a shape and morphs it into the final circle without creating additional scaffolding.
Attachment 122533
Keith's refined method is probably simpler to explain and understand so has to be the current winner.
Acorn
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Re: Double the Area of a Circle
changing the circle to square and back is not something I'd thought of doing, so something for me to take away :)
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2 Attachment(s)
Re: Double the Area of a Circle
Quote:
Originally Posted by
Acorn
My approach was to clone the circle and with the QuickShape tool change the clone to a square (create polygons, 4 sides).
Shift-dag a corner until the square is the same width/height as the original circle.
Final QuickShape tool change square back to a circle (Create ellipses).
My method clones a shape and morphs it into the final circle without creating additional scaffolding.
Attachment 122533
Keith's refined method is probably simpler to explain and understand so has to be the current winner.
Acorn
I'm a bit late to the challenge but have posted a similar method as above I used.
Stygg