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 Triangle**s, 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, a^{2}+b^{2}=c^{2}, to find the last length.
They found that Trinity’s height was √3 feet. They found this by doing the
following:

a^{2}+b^{2}=c^{2}

a^{2}+1-1=4-1

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 90^{o} angle, or a
right angle. Then they measured her bottom right angle and found it to be 60^{o}.
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 180^{o}. They found
that the last angle is 30^{o} by doing the following:

90+60+x=180

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.