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This Challenge it to present three overlapping circles whose centres touch the edge of the other two circles.
Again, the construction is to be as simple and as accurate as the Xara Desktop application allows.
This time, any of the circles can be cloned for use in your construction.
You can assume the solution of the previous two Circle Challenges or start afresh.
Attachment 122446
Acorn
Are you sure the example image is correct, as the edges of the other 2 circles are quite far away from the actual center of the circle
The way I would do it manually would be with help of equilateral triangle, and the radius of the circles would then be the same as the length of the sides on that triangle.
My bad, in my haste I forgot to recheck:
Attachment 122455
Sorry to be awkward, nothing other than circles.
Acorn
Same as my "Three Touching Circles" solution except Nudge = 100
Open Options
Units > Set Units to Pixels
General > Set Angle Constraint to 60 and set Nudge size to 100
Draw Circle > Edit size on Infobar to 200 x 200
Clone (CTRL-K) twice
Select one circle > Nudge Left
Marquee Select ALL > CTRL-Rotate to 60° anti-Counter-Clockwise.
Select top circle > Nudge left
Colour to suit.
Screen transparency using red, green, and blue produces white. Additive color. The areas of overlap produce Cyan, Magenta, and Yellow. You can't make this stuff up.
Gary ... How did you calculate 300 x 286?
Heh heh. I cheated. But it works. I was never good at math.
At first I thought it would be 300 x 300 but that did not work. So I reverse engineered the problem.
...I remember Venn!;))
Well done all!
Sorry Gary, no rectangle allowed, only circles.Quote:
Originally Posted by gwpriester
Acorn
You never said we could not use rectangles. It is my math for the math-challenged solution.
Gary, my bad. I thought the intent was clear inQuote:
Originally Posted by gwpriester
There was an implicit back-reference to the other Challenges that was implicit, not explicit.Quote:
Again, the construction is to be as simple and as accurate as the Xara Desktop application allows.
This time, any of the circles can be cloned for use in your construction.
Acorn
Well also I think you were looking for how different people do things, no? When I was an art director and used magic markers and Pentel to create my advertising layouts, when I needed to center something on the page, like a headline for example, I made tick marks on a separate piece of paper the width of the headline, then folded it in half to determine the center. Again this was what I called math for the math-challenged.
Wholly accepted. My solutions only require an understanding of symmetry, intuitive but a high concept in mathematics. No numbering involved so very similar to your symmetrical folding.Quote:
Originally Posted by gwpriester
Acorn
Here's an all circle method:
Okay, why 55.3% ... since it's very specific, there must be a reason?
I also don't believe that you've completed the challenge ... "This Challenge it to present three overlapping circles whose centres touch the edge of the other two circles."
Do your centres touch the edge?
Spot on Keith, the factor should be 62.88% to get the centres touching. Woods & Trees etc.
Not 100% correct, but I'll be back!
63.44% is the closest I can get ;)
VIDEO
Great challenges Acorn. Brain teasing.
Here's some intesting images made from the challenges:
Fascinating Egg. You can begin to see how the Alhambra Mosque tessellations and friezes are built up.Quote:
Originally Posted by Egg Bramhill
As its builders didn't have calculators, I suggest that any of our solutions involving sums are going to not pass my success criteria.
As your images here demonstrate: symmetry.
Acorn
It annoys me that I can't work out the exact mathematic formula required to set the required factor (in my youth I'm sue I could have ;) ) I can only do it via ratios now and that tends to be hit and miss and not mathematically correct, just a close proximety.
With Snap to Objects set, clone a circle and align the two horizontally so the centres snap to the other's edge.
Clone again and snap the centre of this third with either of the two intersections.
This final placement is a little tricky so I just zoom in and switch to Show Rotation Handles (a crosshair appears) and then I use the arrow keys with Alt to zero in.
Done.
Acorn