# Category Archives: Math 10

# Desmos Portrait Math 10 FPC2019

Here is the link to my Desmos Portrait Project:

**Write-Up**

I tried to use a different type of expression for each body part, and I think I succeeded in doing so. For the head and eyes I used the circle relation. For the nose, I used lines relation. For the mouth and hair I use polynomial expressions (parabolas). For the eyebrows, I used the square root expressions, and for the glasses I used a mix of circles and lines relations.

It took me quite a bit of time to move around each body part, but I realized that if I added constant terms to some equations and coefficients to other terms, I could make the body parts move to the places I wanted them to be in.

I did not have any major challenges, except for having to experiment with different numbers until I came up with just the right one. Other than that, I had no other major setbacks that interfered with my project.

When I started doing the project, I would always have to check back on my notes to remember how to do each equation, but then I started memorizing how each of them worked, so that then I could easily move each of the shapes around without having to check back every time, so I’m proud that I was able to do that.

I did not get any help, mostly because I wanted to see how much I understood myself. My parents did offer to help me, but I refused, because I wanted to memorize the equations myself. Besides, I think I did I much better job than I would’ve done with my parents help. The only help I got was from the internet in the beginning, because I used to check different ways people did their body parts in the past, and then I would choose the design that I liked the best and I would try to recreate it.

I think that overall, this project has helped me learn a lot more about how exactly parabolas worked and how changing just one number in the equations could change the entire graphic. When we first learned them in class, I was a little bit confused about how each relation worked and why they were all so different, but through doing this project, I think I gained a lot more knowledge on the relations, even though I had to figure them out mostly by myself.

# Graphing Story 2019

For this assignment, our group (Simon, Kiara and Fanny) decided to graph how many leaves we could see in the frame of the video in 15 seconds.

Our independent variable was time, as time is continuous, and so our input was seconds, or x.

Our dependent variable was the number of leaves in frame, and our output was number of leaves, or y.

The domain values: x∈{0≤x≤15, x∈R}

The range values: y∈{0,1,2,3,4}

This is the video we created and used for the graph:

This is the graph that I created.

# Flag Pole Lab Math 10 2019

Height of the group member’s eye level : 1.7m

How far away from the flag pole they were standing :4m (add an additional 0.12 m because the base of the flagpole is thicker at the bottom.

The angle of inclination using a clinometer to measure: 60°

**Data & Calculations**

**Results & Conclusion**

5. We had quite a few considerations to take while completing this lab. One of the things we had to modify a little bit was the distance in between the person standing and the flagpole because the base of the flagpole was a little bit thicker, so we had to add an extra 0.12m to the distance. Another consideration we had to take was the eye height from which we were measuring, since we needed to add that height to the total height of the flagpole.

6. With most groups that we compared our answer to, their answer was pretty close to ours, so we were quite sure we measured it right. There were a few groups that had a slightly different answer, but the difference was no more than 1m. I think that the reason there were differences was because the clinometers were really hard to read, and everyone had a different angle, since most people just approximated the angle. Other than that, I think we did a pretty good job at accurately measuring the height of the flag pole.

7. Trigonometry can be used to measure very high things, that they cannot measure with a meter stick, or even those things that are too hard to measure. I think that when we measure things that are very high, we can easily determine the distance we are standing from it by simply measuring with a meter stick. Measuring the angle will be harder, but it is possible, with devices like clinometers. So if we have the angle and the distance that we are standing from the object, we know enough information to calculate its height.

# Infinite Thoughts

**What do you know about infinity?**

Currently, what I now is that there can be different sizes of infinity, and although it makes your head hurt, it is possible to somewhat calculate infinity. I also know that there is a way to have infinity as a sign in some formulas, however what I do not know is how to calculate the formulas. That is something that I wish to learn.

**What new things have you discovered?**

Before, all I thought infinity was was just some sort of way to explain the fact that numbers can go on forever, just to not make our brains hurt. Then, I saw it as a sign in a formula and I realized that it actually meant a lot more than just that. What I discovered is that there are many ways to measure infinity. Although it is “infinite” and can go on forever without a clear ending, there are a lot of interesting and mind-blowing ways that I learned that mathematicians have created so that it is easier to calculate infinity.

**How can you explain/makes sense of different sizes of infinity?**

For me, it is a little easier now to wrap my head around the fact that infinity can be different sizes, so how I make sense of it is that I imagine people just picking up handfuls of numbers, just like when I pick up sand, because the number of sand pebbles are almost, or at least they seem, infinite. I can pick up different sizes of sand handfuls, so that must mean that I can “pick up” many different sizes of infinite numbers, too.

**What are countable infinities? What are non countable infinities?**

From what I have understood, a countable infinity is basically all the numbers that you can count, or at least the numbers that you can imagine in a pattern (like if you were to double every number, you can imagine the answers). Non-countable infinities are all the other infinities that are usually either impossible to count, or they are so long that it would take forever to figure them out.

**What questions do you still have about infinity?**

I think that my only question about infinity is how many different was there are to “measure” infinity. I learned quite a few that I though were quite interesting, however I know that with the numerous amount of mathematicians who have tried to count infinity, there must be millions of ways to do it.

# Love Poem to Prime Numbers

```
The rules of prime (a sort-of Love Poem to prime numbers, written in only haikus)
By Fanny
Only can divide
By itself and a one
Is a prime number
Weird, they said often
That there are forty-six
In one - two hundred
Five and Seven too
Or even Seventeen
Are part of the group
Interestingly,
There aren't many patterns
To make it more easy
Multiples of Three
Are quite easy to find
All is simply:
Add all the digits
That make up the number
Next, look at the sum.
Is it a nice sum?
If it's divisible
By the number Three,
Then you know for sure
That it's a multiple
Of the number Three.
What about the Two?
That rule is much more simple.
Is the number even?
If so, the number
Is divisible by
The nice number Two.
Finally, now comes
The rule for number One.
It is a weird one.
It is not a prime,
It's not a composite,
It's absolutely
NEITHER!
```