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Sunday, 20 February 2011

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.

19 comments:

Jo Davies said...

Beautiful card love the flowers and the backing paper goes together just beautifully... gorgeous! JO xxx

ona_i_ja said...

Josephine, your card is adorable! I love colours you used!
Hugs
Agnieszka

Carol Ann said...

Beautiful card the colours are just gorgeous! I could never have managed the maths :)

Carol Ann x

Teri said...

Gorgeous hun! Love what you did with my Crocus image - super colouring!
Sorry though, brain glazed over with the maths bit. . . LOL
Hugs,
Teri x

Nannieflash said...

Wowee Josephine that is a stunning card, love the colour choice its my favourite. With love and hugs Shirleyxxxxx

Debs said...

Wow!! love it, gorgeous colors and die cut and beautifully colored image
Debs
xxx

KraftyKoolKat said...

Gorgeous. Thank you for sharing with us at Digi Doodle Shop's Best.

Hugs
Cathy
xxxx

Fleur said...

Wow this looks great, The colours are lovely & a pretty image
Thanks for joining my nature challenge at ALLSORTS this week, Good Luck
Hugz Fleur xXx

Annette Bowes said...

Purplicious Josephine! Beautiful image, papers and love the Octagon shape, take careX:)

xxxtglxxx said...

This is a WOW card!! Oh My, I adore this. Gorgeous deep colours, such a pretty image and a very creative shape :)

Your colouring is beautiful.

Thanks so much for visiting my blog and your comments, I have never heard of Rymans, but I will look out for it.

hugs

xxalisonxx

Rebekah said...

Fantastic work Josephine! I love the colours here and your shape is fab! Hugs Rebekah xx

Pink Sunshine said...

Beautiful spring card, thanks for joining us at Charisma.
Sally. x

Anne-Marije said...

What a nice card!
Thanks for your participation in the Digital Tuesday Challenge...
xxx Anne-Marije

Vicky said...

Just so beautiful and I love the colours you have used Josephine :o)

thank you for joining us at totally papercrafts and good luck!!

hugs Vicky xx

Floppy Latte Designs said...

Wow! The coloring and shape of this one is fantastic!

Hugs, Jess

Nicecrane Designs said...

Love the purple tones and all over these folded butterflies,,,wowwww,,,,,,very well done.

Love crafts forever said...

This is my Favorite card. Love it.
Hugs Nat

Tracy said...

beautiful card, the shape and colours look fab and i love the butterflies. Thanks for joining us at The Creative Cottage, Tracy x

Marjo said...

I love, love the colors Josephine, gorgeous card!

Hugs, Marjo

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