Tuesday, September 25, 2012

Math Stories: Special Triangles

Two weeks ago I was introducing the special triangles (with angles of 45-45-90 and 30-60-90) in my pre-calc class, and on a whim, I asked them to make up stories with those two triangles as characters. Only about a dozen students did the assignment, but what they created was really fun to read. A few students have given me permission to share their stories here. I'm sharing those 3 stories below. I may get to share a few more later.

This post is my birthday present to myself. Anyone else want to share some math stories?

Different Views of Shapes, by Aldrich Pablo
Once upon a time, there was a square name Geo. Geo was a hard working square who worked in the slaughterhouse. Geo loved his work. He loved his work because his wife, Tri, an equilateral triangle, also worked at the slaughterhouse alongside of him.  Like any other day, both Geo and Tri cut fellow square and triangular shapes vertically and diagonally, making sure they cut them into 2 different types of triangles, a 45®-45®-90® triangle, derived from the squares, and a 30®-60®-90® triangle, derived from the equilateral triangles.
One day however, Geo got accidentally pushed into the cutting machines by his enemy, Bre, the circle. With the affectionate love Tri had for Geo, Tri jumped in and tried to save Geo. But it was too late. Both Geo and Tri have been sliced diagonally and vertically. Geo became a 45®-45®-90® triangle, and Tri became a 30®-60®-90® triangle.
Even though Geo and Tri got sliced in half, they both wanted to do the same to Bre. With all the mixed emotions both triangles have, they were able to learn something new about each other. Geo, the 45®-45®-90® triangle, learned that he still has the same leg lengths, but half of the original shape. Tri, the 30®-60®-90® triangle, learned that she is just half of the original shape, forming different angles.
With previous shapes that have been sliced by the workers, Geo and Tri were also able to understand that with their new shapes, multiple of the same shapes together form a circle. Bre was horrified. Once Geo and Tri were able to understand their new shapes, they too, pushed Bre into the slaughter machines. Because of a malfunction when Bre went into the machines, Bre got stuck, and the machine exploded.
When the machine exploded, both Geo and Tri saw him fly into the air. When both triangles went to go look for him however, Bre was nowhere to be found. They believe that Bre became the sun, and he was never to be seen again. So every time when Geo and Tri go to work at the factory, they will always remember Bre, as they look towards the sun.
The End.

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The Story of the Special Right Triangles, by Miranda Barron
Once upon a time, there were two special triangle cousins, one named Mr. 45, full name 45-45-90 Triangle, and the other named Ms. 30, short for 30-60-90 Triangle. These two cousins both inherited their family’s 90° angle trait yet they each were very different and special in their own way. Mr. 45 had two legs that were equal lengths, meaning he also had the equal corresponding angles. If Mr. 45 could walk he’d walk like a human. Hard to believe, isn’t it?  Well Ms. 30 wasn’t so lucky as to have equal lengths. She had to constantly ask for help from her cousin. It was a hard life for her, but she never let it bring her down.
The reason she learned to live with it was when she had kids. Each kid had different sized legs just like her. They even had the same proportion. She was always able to find the sizes of pant legs for her kids without having to measure each child’s leg, since it made them feel self-conscious. Each child, like her, had a proportion that had to do with one leg being x inches, then the other leg was x√3 inches, to go with the rest of their body that was 2x inches. It was the magical method to go with their cursed life.
On the other hand, Mr. 45 and his kids weren’t so unique. He still found a way to make his children seem special with their normal equal length legs. He found that each of his kids were proportioned like him. Each of their legs would measure x inches to go with the rest of their body that was x√2.
This seems like a weird story but it shows how unique and special you can be when you’re different. Mr. 45’s kids never got their pants personally made, one reason being their dad refused to sew, while Ms. 30’s kids got to have personally made pants from their loving and caring mother. Being special is amazing and that’s how things should be for everyone and everything. :D

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A Special Triangle, by Ayesha Saleem
Isis is a triangle and her friend, Trinity, is a triangle who is also a conjoined twin. She is conjoined with her brother and together they are an equilateral triangle, which has three congruent sides and angles. About two weeks ago, Trinity and her brother underwent a rigorous surgery to get separated from one another. They had to stay in the hospital for a little over a week so that the doctors could keep an eye on their recovery. The siblings were allowed to go home yesterday, and today Isis and Trinity went to the park to hang out. Isis wanted to see how her best friend was and how she looks now that she is not connected to her brother by one side.
They met at a local park where they used to go to a lot when they were younger. Isis was so shocked at how differently Trinity looked. She was so happy that she has been recovering well and that she is happy with the surgery. Trinity brought along a measuring tape and a protractor. She wanted Isis to help her measure her sides and angles since she didn’t know what their measurements were anymore.
Isis wanted to start by measuring her sides, so they started with Trinity’s base. They measured in across the bottom to be one foot long. Then they measured her hypotenuse, which was two feet long. Now they had to measure her height. They measured it and it came out to be a weird, decimal number. So, to be more exact, they decided to use the formula, a2+b2=c2, to find the last length. They found that Trinity’s height was √3 feet. They found this by doing the following:
a2+b2=c2

a2+12=22
a2+1-1=4-1

a2=3
a=√3
Next, they moved on to measuring her angles. They stared with the angle made between her height and base. They used the protractor and measured that it was a 90o angle, or a right angle. Then they measured her bottom right angle and found it to be 60o. Since Isis couldn’t reach up to the last angle at the top of Trinity, they decided to do it mathematically. They already knew that all triangles have three angles that will always add up to a total of 180o. They found that the last angle is 30o by doing the following:

90+60+x=180

150-150+x=180-150
x=30
After doing all the measuring, they discovered that Trinity is now a Special, 30-60-90, Triangle. Trinity was so surprised; she didn’t think that she deserved to be a Special Triangle! Isis congratulated her and she was happy for her best friend. Trinity suggested that they measure Isis and maybe that she is also a Special Triangle, but Isis said she already knew that she was an Isosceles Triangle, meaning she had to equal sides and two equal angles. Isis was fine with being an Isosceles Triangle and Trinity was happy to find out that she was a Special, 30-60-90, Triangle.