Introduction: Making a String of Pennant Flags Using Math

My mom calls this project “Fiesta”, because it reminds her of celebrations as a little girl in the Philippines. In any case, it is a great way to liven up a room in preparation for a party or in general to just brighten your mood. It also might come in handy if you want to open a used car dealership.

Step 1: Choose the Room You Want to Decorate.

The math required for making a pennant flag is very precise and will save you from a lot of extra work and wasted materials.

Step 2: Measure the Perimeter of Your Room.

Start by creating a diagram of the room you want to measure. Even if the room is perfectly square, you want to draw this picture and write your measurements on it. It is useful if you are going to have people help you. They will be able to see the diagram and understand what you are trying to do.

Add all of the measurements and you will have the perimeter of your room.

If you measured your room in feet like I did, don't forget to convert that to inches. You can do this easily by taking the measurement in feet and just multiplying by 12. In my project, the total perimeter of my decorating room is 56.6 feet or 679.2 inches (56.6 x 12).

Step 3: Choose Your Pennant Materials.

You can use any size pennant material! What you choose though is related to how much work you will need to do later. Plus, if the material is already square, it will save you a whole step in cutting.

For my example I used a very colorful pack of papers from IKEA.

Step 4: Measure Your Pennant Materials.

The best material will be light but more importantly it will be square or at least rectangle. Measure both the length and the width. We are going to keep the measurement of the shorter side, because the longer side will eventually cut down to make each sheet a perfect square.

Step 5: Do the Math; Pythagorean Theorem and Square Roots by Hand.

The Pythagorean Theorem, in a right triangle is a² + b² = c². In our special case since we will have a perfect square, the version of the Pythagorean Theorem we are going to use is 2a² = c², because two of the sides are the same size.

In my project example, my sides are 8.25". Your measurements may be different. We calculate to find that our pennant flag size is approximately the √136 (square root).

Calculating the square root of a number by hand, you need to locate the perfect squares around your number and use the smaller value. In my example, the √136 is between 11 (√121) and 12 (√144). Here is where we get our first decimal of precision.

136 ÷ 11 = 12.36

Average 11 and 12.36 or (11 + 12.36 ) ÷ 2 = 11.68

We want at least two points of decimal precision. So, we are going to perform that math again with our new square root value of 11.68.

136 ÷ 11.68 = 11.64

Average 11.64 and 11.68 or (11.64 + 11.68) ÷ 2 = 11.66

My pennant size or hypotenuse C ≈ 11.66 inches

Now we take our total perimeter from Step 2 of 679.2 ÷ 11.66 = 58.2 pennants, or 59 whole pennants. This has to rounded up again to the nearest even number, because we are dividing each material into pieces. 59 to the next even number is 60. Divide this number by two and you will have the number of sheets of material you need.

Step 6: Cut the Pennant Flags.

If you bought rectangle material that was already square you can skip cutting the material sheets into squares and go the next cut. Now cut the squares diagonally.

Note: You will not need any more pennants than what you calculated. Try to save the material for other projects.

Step 7: Tape the Pennants to the String.

You can measure out the perimeter of your room in string, but it is faster to just start taping your flags on to your string. I calculated 59 whole pennants to cover more than our string, but really we just need 58 pennants.

Start by taping the string to each hypotenuse corner of each flag and then put one piece of tape in the middle for extra support. Remember to keep in mind the side that your are taping your flags on. You want to keep them all taped on the same side as the other. This is very important if you have specialty paper that only looks cool from one side and not the other. As you add more flags make sure to make your hypotenuse corners of your pennant flags touching the flag you attached before.

Step 8: Tape the Pennant Flag String to the Walls.

You should be able to use thumb tacks to pin up the flags, but my mom doesn't want me to be making holes in the wall. My only choice is to use tape for each and every pennant flag.

Step 9: Enjoy Your Fiesta of Pennant Flags!

Don't forget to look up and have a party in your heart every day or even every hour!