Double the Area of a Circle

[Acorn]

Using any Xara tools, can you create a circle and without any calculations render another circle to be double the original circle's area?



Acorn

[gwpriester]

Two ways.

[Acorn]

Two ways.

Gary, I think you have increased the area fourfold.

It is not clear when and why I would stop dragging.

Acorn

[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...

[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

[Acorn]

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

[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

[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

[Acorn]

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

[Acorn]

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