Friday, June 13, 2014

Flower Cupcake Bouquet and a Bit of Math

Next week on Tuesday evening at 7:30pm I'm offering a Flower Cupcake Workshop. At the moment there is one spot left- contact me if you'd like to join us. During the workshop, besides learning how to make five different kinds of flowers, everyone will also enjoy snacking on cupcakes. Recently I found this example of a cupcake bouquet and had to try to make my own for the workshop snacking purpose. First, I made a bunch of mini-cupcakes and frosted with buttercream, tip 104 in a carnation style. I experimented with different sized pots and ultimately decided on a mug to hold my bouquet because it was the right size. I needed a nine centimeter foam ball but did not have time to get to a craft store so I cut a florist's block and covered it with two layers of heavy duty tissue paper.
Next, to add to the stability, I filled my Dutch mug with smooth stones because I couldn't find my daughter's glass marbles I was hoping to use.
I cut bar-b-q sticks to size and jammed three into the ball and the other end down into the rocks in the mug. I was worried one stick would not be strong enough.
I cut a stick for each cupcake and, starting with the very top, placed each cupcake by jamming one end of the stick into the green ball and the other (pointy) end into the cupcake.
 I had to reposition some cupcakes after I realized I placed them too far apart. The key to the placement is measuring the diameter of the bottom of the cupcake (for my mini-cupcakes it was 3.5cm) and using half that distance away from the nearest cupcake for the next stick. It feels too close when placing the stick but it works. Incidentally, this cupcake bouquet is not for Tuesday- it is just a test bouquet. I'll make a fresh one the day before the workshop.
For the finishing touch I added some leaves using tip 68.

But what about the math, you ask? In determining how big of a foam ball to use, I had to decide how many cupcakes I wanted to display. Since I had made 24, I thought perhaps around 20 or 22 would work (always have extra for the hungry mouths around here.) I only wanted to do about 2/3 of the sphere because 1/3 would be underneath of course, so a 32 faced polyhedron seemed about right. Google gave me this equation:
where r is the radius of the sphere and a is side of a six sided polygon (okay it isn't a circle but its close) packed on that sphere(polyhedron- we're being a little fuzzy here).
Pretending for a moment that this polygon is the bottom of the cupcake I used circumfrence = 6*a and then:
rc= 6a/2Pi
Where rc is the radius of the circle or cupcake.
Solving for a yields:
Substituting this into the above equation:
My rc (radius of the cupcake) was 1.75cm. Solving for r gave me 4.5cm or a 9cm diameter ball to give me enough room for 22 cupcakes.

I did not have a 9cm ball, however.

Not to be deterred, I had a piece of floral foam which was 7cm on the shortest side so I cut a 7cm block and kept shaving off the corners until it was a ball. I used a total of 16 mini-cupcakes on the 7cm ball. If you feel like doing more math to calculate the equation for a 7cm ball feel free. I'm going to bed.
 There you have it: math and cupcakes.