One Stitch at a Time Challenge 50

This week at One Stitch at a Time, we want you to show us your shapes! And none of them are to be squares.

We're sponsored this week by Joanna Sheen who's offering a £10 voucher to the lucky winner, and she offers free worldwide postage!

The theme this week was Natalyia's bright idea - no squares. Definitely something that takes me out of my comfort zone. So ... what did I do? I turned a square into an octagon!

The inner octagons were cut with my Nesties, but the scallopped one is the largest in that range. So, to cut the card, mat and paper bigger than that, I had to use some Maths! (I'll put a bit of that at the end of this post so as not to  bore those of you who're not interested!)

The gorgeous image is from Delicious Doodles and is available at the Stitchy Bear store. I coloured it with Promarkers, but added some extra shading with my new Coloursoft pencils. The backing paper is from the Flower Power CD which I got from Crafty Emma's store. The butterflies are die cut - not sure whose die maybe Quikutz? I've covered the lower layer with some fantasy film and used the fact that the die doesn't cut too well, leaving all the cut out areas in place. The upper layer is thin card which did cut properly, coloured with Promarkers.

I'd like to enter this card into the following challenges:

Digital Tuesday who want die cuts (the various nesties used in layering and the butterflies)
Bunny Zoe who want Spring Flowers
Creative Cottage whose theme is Fabulous Florals
Charisma Cardz whose theme is 'Spring has Sprung',
Totally Papercrafts who want digis
Digi Doodles where 'Anything Goes',
Mami Doodles who have a Flower theme,
Allsorts who have a 'nature' theme.

Now, the Maths. I'd be really interested to know if this is useful to anyone. And if you spot a problem or don't get what I'm doing, please let me know.

I started with a square card - I measured it at 148mm square.

To cut an octagon with sides all length a mm, we need to find out the measurement b mm. The external angle of an octagon is 45`as marked.

We know that a + 2b = 148mm.
From basic trigonometry, we know that sin(45`)= opposite/hypotenuse of the right-angled triangle = b/a.
or sin45=b/a
which gives b=a x sin45.

Substituting this value for b into the first equation gives:
a + 2(a x sin45) = 148 mm
a(1+2sin45) = 148 mm
a= 148mm/(1+2sin45)
Using a calculator, a=61mm (rounded)
Therefore, from a+2b =148 mm,
b= (148-61)/2 = 43.5mm.

So, to cut an octagon with 61mm sides, you need to cut the corners off your square, 43.5mm from the edge of each side.

Doing the same calculation for different square sizes gives the cut points for different sized octagons.

In general, a= L/(2sin45 +1) and b= (L-a)/2 where L is the length of side of the square in mm.
Or, if you don't like the look of ths trig function,
a=L/2.41, and b=(L-a)/2.