£2.00

Become a Member for free access to this and other files on the site.
See the Membership page for more details.

Already a Member? Log in Here

The donut/doughnut model is a fun model, quick to make and fantastical!

Although it was originally designed to have 11 segments it actually works better with only ten. As a member you can download the parts file at the end of this post.

Print out the appropriate number of either mono or colour parts sheets onto thin card.. Score along the dotted lines and cut out the parts. Roll each section round and glue it down to make a wedge shape .

Glue the sections together. Be careful to do this accurately.

Glue eight of the basic sections together to make the body of the torus.

Carefuly glue the two end pieces into place as shown.

Glue the large tabs down to complete the model. If you glue them down carefully they should be virtually invisible.

That's it! You now have a paper Donut. I'm not sure what you can do with it but it look great doesn't it! Its got to be useful for something!

Keep up to date: Receive the latest blog post by email

Closing the donut shape is tricky, You really need detachable fingers or the help of a dexterous mouse. As I say - tricky.

William H suggested using two sets of tabs on the final joint, this works well in some circumstances but unfortunately as the tube is an octogon in section it is collapsable. This makes it really hard to keep everything lined up as the glue is drying. So instead of that I've tried putting the tabs on the outside. To hide the tabs I've made them as large as the adjacent faces. That way they cover the faces completely with the edges lined up with the edges of the model.

In this model I've created a final section with these oversize tabs.

This piece is glued into place last. There is enough flexiblity in the model to let me glue the final section on fairly easily.

...then by gluing the flaps down I can close the circle. 

In the final version I have four large tabs on one side and the alternate tabs on the other end.

It all works rather neatly. Okay - model done - download post to write up.

Keep up to date: Receive the latest blog post by email

I've finished sizing up the Toroid model today as well as getting the new look web site ready for roll out. Busy day!

The toroid model had loads of fun maths in it which I've gone over below. Enjoy.

Okay - so I'm breaking the fourth wall but really, how are you supposed to take pictures with your left hand?

I've divided the donut into 11 wedges, each made from an eight sided shape. I know that the angle of each section is approx 32.7 degrees. (360/11) To create each piece I need to work out the minimum height (h1), the maximum height(h2) and the length of each of the faces (L)

Okay - L first.

I'm aiming at a donut with inner radius of 20mm and an outer radius of 75mm. That means that the actual donut body (d) has a diameter of 55mm (75mm-20mm) Using trig above that means that the length of each face is close enough to 21mm as makes no difference. (sin 22.5 x 55mm)

So that's L sorted.

For the two heights I'll switch to a plan view of the donut. I've already established that the angle is 32.7 degrees. I'll use tan this time because I'm looking for the hypotenuse. So,  tan 32.7 is 0.642. To work out the two heights I just need to multiply the two radii by this figure giving: h1 = 13mm and h2 = 48mm.

So there you have it - donuts by numbers - and that's why I love maths.

Now I just need to print out eleven of these and hope that they stick together correctly.

That'll have to wait - friends visiting.

Keep up to date: Receive the latest blog post by email

I've been experimenting with doughnuts of different dimension. I think I'm going to go for one with a slightly larger ring in the centre than the one here. That'll be tomorrow as I'm taking #1 son out to the theatre so we can play with the lights. Should be fun!

I had written a post yesterday about the mathematics of the torus design - but managed to loose it. If you follow me on twitter you proabably heard that I posted it- multiple times! I'll have another go at uploading it, the maths behind the model is really interesting and it is good to share!

If you receive the blog posts email you'll have noticed the <!--break--> tag in the middle of the text. It was trying to get rid of that that killed the maths post. I have a couple of other solutions so fingers crossed the stray tag should be gone soon.

Keep up to date: Receive the latest blog post by email

I received the by now traditional Simpson socks for Father's day and as you would imagine, this got me thinking about doughnuts. A quick search on google turned up nothing by way of toroid nets. Time to get the brain into gear. I had a vague memory of a toroid shape made up of sections in an advert for Mathematica, but how to design the section?

Each section is a kind of circular wedge. The net for that would have a sine wave edge. So, create sine wave, sample 360 degree section of same, stretch to appropriate size.

I then flipped over a copy, added evenly spaced vertical sections (8 of them) and created the net for a single section complete with tabs that you see above.

It worked surprisingly well! Notice that even though the edge is based on a curve it sits nice and flat on the work surface. Lovely.

There is a certain amount of guess work involved here. How steep should the angle of the wedge be? How many sections will I need? These two numbers are connected but I'm not sure how. Time to cut out and try.

I glued six sections together and created this shape which looks like it is just short of half a doughnut.

Too save time and cutting, here is the same shape held up to a mirror. Two more sections I reckon, making fourteen in total. I'm really not sure how I'm going to glue the last piece into place!

Fourteen seemed like a lot of parts so I tried the same again but with much thicker wedges. The result is in the square photo at the top. Looks like seven wedges for a complete shape . Looking at it, though, I think the fourteen wedges are worth the extra effort.

Colour and sprinkles next!

--------

I've added the file with the parts as they are so far if you want a try. Member's download below.

Keep up to date: Receive the latest blog post by email