Constructing Christmas Trees

Sun, 11 Dec 2011

The Christmas tree project that I am working on at the moment uses a series of cones to form the branches. How to join the naturally circular cone to a square section tube? Time to break out the maths!


The lowest cone on the tree is make by wrapping round a three quarter circle of paper. A full circle is 360° so 3/4 of a circle is 360 x 0.75 = 270° 


On a flat circle, to cut a square hole in the centre, each side of the hole is rotated 90° compared to the previous side. For three quarters of a circle we'll rotate each side three quarters of ninety degrees.

0.75 x 90° = 65°

And we end up with this open sided shape. (below right)


I've fitted the freshly minted shape into the cone – shown in red below. I just need to add some tabs and it will be ready to print out and go.


Works a treat! I scaled the cone up ever so slightly (103%) so that it is a loose fit and glued it into place on the top of the tube. The middle cone has a slightly different angle so the inner shape will need recalculating but the top cone has no hole so that one will be simple!

Maths. It works.

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Comments (3)

  • maxlrainer December 11, 2011 at 5:30 pm

    Great, I like those

    Great, I like those geometrical  interludes.

  • frankenpaper December 12, 2011 at 11:48 am

    I like the way you explained

    I like the way you explained the math. You make it seem easy.

    • robives December 12, 2011 at 6:59 pm

      Thanks chaps, glad you liked

      Thanks chaps, glad you liked it 🙂

Comments are closed.