Jerry & Max responded that they want to do the Triangle Banner with stars. That is a good choice. There is only basic sewing for the panels, and the Star templates are already cut. The Star is an easy first-time applique project.

It is Auralie's job to do the math so that the banner panels are cut to the right size. Since we are making a 6-foot banner, what size Squares should be cut to make the Triangles?

The Triangles are made from squares, which are cut in half along the diagonal, with the diagonal of the square(s) against the pole for the banner. In the example above, there are two triangles against the pole. That tells us that each diagonal is 36" (6 feet = 72". 72/2=36) Okay, what size square is needed to provide a 36" diagonal?

Have you met my friend, Pythagoras? He has a Theorem that says that for any right (90 degree) triangle, the length of the hypotenuse is the root of the sum of the squares of each side. Most of us know the Pythagorean Theorem as A

^{2}+ B

^{2}= C

^{2}. Since we know the value for C, but not for A or B, we need to work the Pythagorean Theorem backwards.

Since we are working with squares, we know that both sides are the same length. So, A = B. So we can re-write the Pythagorean as A

^{2}x 2 = C

^{2}. Or 2 (A

^{2}) = C

^{2}.If we divide both sides of the equation by 2, the 2's on the left cancel, and the equation becomes A

^{2}= C

^{2}/2.

Now we know that we can take C (36"), square it (36 x 36 = 1,296), halve it ( 1,296 / 2 = 648), and take the root (Square Root of 648 = 25.45), to find out that the size of a square that will yield a 36" hypotenuse is 25-1/2"", for all practical purposes. (

*Thanks, Max!*)

Don't tell Auralie that there will be a quiz at the workshop.

So - let's look out the options. First, a Triangle Banner with stars aligned to the centers of the triangles:

The stars in this version were moved around until they looked centered. Notice that they no longer line up top to bottom. |

COOL! I like the lower star choice, but give me some red stars, too!

ReplyDeleteSounds like a great first time project. Count us in.

ReplyDeleteJim & Auralie