Physics of Brazilian Jiu-Jitsu

Inquiry Question: How does a Brazilian Jiu-Jitsu practitioner’s understanding of physics make him or her more effective?

Jiu Jitsu is the gentle art. While you do end up breaking peoples bones, it’s the fact that you don’t need 8-inch diameter biceps to beat someone. You actually use their own body against them, through the power of phyiscs ooooooh. By using their own body weight and momentum, you can throw them around, over your body, and have them in a choke. You use forces of gravity, momentum, and other physics to grapple your opponent and send them into an armbar, kneebar, or a number of other chokes and holds.

We examine this fighting style today because the moves that Jiu-Jitsu artists train lie firmly in physics, more specifically, torque and momentum. In the case of an armbar, you use the persons joints and arm against them, and you use your legs as a fulcrum, essentially magnifying the amount of force you can exert on your opponent’s arm.

A kneebar works the same way. You use your legs as the pivot point, and their leg is the fulcrum. Pushing sideways relative to the knee inflicts major pain on the opponent, and your knowledge of physics, more specifically, the pivot point you make with your legs, increases your effective stopping power.

Say you’re a relatively small person fighting a much larger person. Using your knowledge of physics, you know the large man’s center of gravity is much more higher up. You can use this to send him to the ground faster, as the old saying goes, “The bigger they are, the harder they fall.” Once on the ground, take their knee or arm and get them into one of these holds, or a number of other ones and utilize your knowledge of torque and fulcrums to make him cry uncle.

Desmos Art Functions Card 2018

https://www.desmos.com/calculator/hbwdk2dnnx

This was a fun project, as it tested my knowledge of graphing all the functions we learned in pre calc 12, but also how to manipulate them through translations and transformations. Using absolute values for letters, parabolas for my head, and coordinate points for eyes and ornaments were a couple of ingenious ideas I had. The tree had two iterations,  the first one looked weird. For a couple of lines, I used quadratic functions, and reflected them over the x=y axis to make ears. It was weird playing with them at first. They definitely helped, though. Overall, I am happy with the finished product, and the project has deepened my skills with manipulating functions.

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Review of Edublog Plugins

Today, I’m reviewing three plugins that Edublog offers.

Embed Any Document is easily one of my favourite plugins to use. This plugin simplifies the process of uploading and embedding a document of your choice, word docs, powerpoint presentations, you name it. You can upload documents from your laptop, from a URL, from Dropbox or Google Drive. For me, the plugin has almost never not worked, it’s very reliable. I love it, and it’s a must for any student at Riverside who often uploads to their Edublog.

The Tag Cloud also seems to be a favourite for a lot of my peers, as it wonderfully organizes your tags, categories, or both into a neat little cloud for you to rotate to your leisure. At least, that’s what it’s advertised it does. In reality, it simply lists your tags and categories. The more often you use said tags or categories, the bigger they are on the cloud/wall. Unfortunately, I could not get this plugin to work. Documentation for this plugin is also not available, as requesting it on the plugins page leads to a dead link. My view on this plugin; if you’re a function over form kind of guy or gal, why not have it on your blog?

 

Tech Team Reflection 2018

I helped a lot this year. I feel like a did a lot more this year than compared to last year. Where there was about three events that I could participate in, this year I could take part in a large number and I feel like I was valued. I was part of the 2017-2018 boot camp, I helped at the tech night to show parents what devices they should buy their kids for school. And my favourite, I started working alongside Mr. Shen and learned important things regarding computers, information technology, and even some life lessons.

This year, I feel like an important part of the tech team. A reason why I’m grateful that I joined the tech team is that it opened up the opportunity to take part in the Make with Microsoft Program. I learned a lot and I got an amazing opportunity to be not a consumer, but a producer on the BCTech Summit floor.

Pre-Calculus 11 Week 18 – Top Five from Pre-Calculus 11

I’ve learned a lot this year in my math class. This blog post is dedicated to the top five things I’ve learned.

1. Geometric Sequences and Series

Geometric Sequences and Series are pretty cool. You can do some fancy math magic with the formulas. A geometric sequence is when each term after the first term is multiplied by a constant to determine the next term. For example, the sequence “2, 4, 8, 16, 32” is geometric. The common ratio is what the number is being multiplied by. In this case, it is four. The formula to determine a term in a geometric sequence is t_o=ar^{n-1}s=3, with a being the first term, and r being the common ratio.

While a geometric series is when you add all the numbers together up to a certain term. For example, in the geometric series “3, 9, 27, 81”, S_5 is 363. You can calculate geometric series with the formula

2. Graphing Absolute Values

Image result for absolute value graph

 

Graphing an absolute value is pretty cool. It’s almost just like a regular graph, except anything below the x-axis is

reflected above the x-axis. They look pretty neat, and you can do this with linear and quadratic equations! An equation with absolute values looks something like y=|x+3|.

3. General Form, Standard Form, and Factored Form

So there’s three different forms of quadratic expressions and equations. You’ve got general form, which is the one that we tend to see the most. You’ll remember it from grade 10. ax^2 + bx + c. Standard form is my favourite, as it is tends to give you the most information. You can see the scale, the horizontal and vertical translation, the vertex, the axis of symmetry, and more! It’s represented with (x + p)^2 + q. Factored form can give us the solutions to the parabola, which is a fancy word for where the parabola intersects with the x-axis. Factored form looks like (x +x_1)(x+x_2)

4.  The Quadratic Formula

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

That’s a mouthful, isn’t it? The quadratic formula is used what you have a quadratic expression that just does not factor nicely at all. While you’ll get answers like x=\frac{-1\pm\sqrt{47}}{3}, it’s actually the nicest answer you’re going to get without a calculator. It’s also the exact answer, since if you put your answer down in decimal, you’re actually rounding off numbers, meaning your answer is inaccurate.

5. Graphing reciprocal functions

They’re SUPER weird. But they’re kinda cool. Reciprocal is a fancy word for flip. For example, the reciprocal function of x+4 is \frac{1}{x+4} Now describing what it looks like is near-impossible to describe… So take a look at it below. It’s scary, and after grade 11 is over, I want nothing to do with it for three months..Image result for reciprocal function

Pre-Calculus 11 Week 17

This week we covered just about everything in our Trigonometry unit, so I am going to attempt to put as much as I can into this blog post.

SOH CAH TOA is updated for x, y and r. I’ll explain.

Sine = \frac{Opposite}{Hypotenuse} is now sine = \frac {y}{r}

Cosine = \frac{Adjacent}{Hypotenuse} is now cosine = \frac{x}{r}

And Tangent = \frac{Opposite}{Adjacent} is now tangent = \frac{y}{x}

The best way to remember these, is to simply remember that sine is \frac {y}{r}. You should know that the hypotenuse is \frac{x}{r}, so

So where the heck did x, y  and even come from? Prepare to be introduced to reference angles and unit circles!

Image result for unit circle trig

Rotation angle is different from reference angle. Rotation angle is how far the terminal arm has rotated from the rest position, 0^o.

Image result for reference angle trig

 

The reference angle is always going to be beside the x-axis. And then from here, we can find out which lines are the

adjacent and opposite lines. Then we can find out which trig ratio to use. For example, the reference

angle for a rotation of 160^o degrees is 20 degrees, because the angle needs 20 more degrees to reach the x-axis. Or, a 225 degree angle has a reference angle of 45 degrees, because it needs to lose 45 degrees to reach the 180 degrees point.

Now, there are special triangles that you should remember as well. These let you do trigonometry without a calculator, and it can also be a way to double check your work.

Image result for trig special triangles

Say, you wanted to find sin 45^o. First, you’re dealing with a 45 degree angle, so you know you’re gonna look at your isosceles right triangle. You know sin is \frac{y}{r}, so that means sin45 is \frac {1}{\sqrt{2}}

Or, you want to know cos 60. You know cos = \frac{Adjacent}{Hypotenuse}, or what we’re really supposed to remember, cos = \frac{x}{r}. This means cos 60 = \frac{1}{2}

 

But obviously, you’re not going to deal only with triangles that have side lengths of 1, 2, and \sqrt{3} units.

How do we fix this?

Well, do you remember similar triangles? From grade nine? I’ll refresh you just in case. If two triangles have the same angles, then that means the only difference between the two can be the size, or the side lengths. This means, if you run into another triangle that has angles of 30, 60, and 90 degrees, but has side lengths of 4, 4\sqrt{3} and 8, then you simply have to find the scale factor! The scale factor in that triangle that I described above is 4. If you divide all side lengths by 4, you’ll get our 1-\sqrt{3}$-2 sides again.

Pre-Calculus 11 Week 16 – Trigonometry Review

We finished our Rational Expressions and Equations test this week, so we’ve started our new unit. Trigonometry. So I’m gonna post everything I remember from Trigonometry in grade 10.

Image result for triangle trig

In a right triangle, the side closest to theta that isn’t the hypotenuse is the adjacent side. The side farthest is the opposite side, and the hypotenuse remains the same, like always.

Remember SOH CAH TOA

SOH is Sine = \frac{Opposite}{Hypotenuse}

 

CAH is Cosine = \frac{Adjacent}{Hypotenuse}

 

TOA is Tangent = \frac{Opposite}{Adjacent}

 

To find an angle when you have the lengths of two sides, you can use the inverse of sine, cosine, or tangent. Image result for triangle sidesSay you had this triangle. You want to find the angle of B. Well, that makes the 5cm side the opposite side, and the 7cm side the hypotenuse. We don’t know how long the adjacent side is, so we can’t use that. So which ratio can we use? We can use Sine, because Sine = \frac {Opposite}{Hypotenuse}

So to find the angle of B, we take the inverse sine of 5/7.

 

And of course, with some algebra skills, you can also also find the length of one side if you have the length of another side and an angle.

Don’t forget, you can also use the Pythagorean theorem to find the length of another side if you need to.

Pre-Calculus 11 Week 15 – Solving Rational Equations

This week, we solved rational equations

Note that this is different from last week, where we only simplified rational expressions.

Simplifying looks like this:

\frac {x^2+5x+6}{x+3}

 

\frac {(x+2)(x+3)}{x+3}

 

x+2

And solving looks like this:

\frac {x^2+5x+6}{x+3}=

 

\frac {(x+2)(x+3)}{x+3}

 

x+2

 

x = -2

 

The major difference here is the equal sign that is present when solving vs no equal sign when simplifying.

A common issue with solving ration expressions is how to add together two or more fractions when they have different denominators. Simply remove the denominator like so

\frac {x-1}{x-3}= \frac{x+1}{x-4}

 

\frac {(x-1)(x-3)(x-4)}{x-3} = \frac {(x+1)(x-3)(x-4)}{x-4}

 

x^2-4x-3 = x^2-2x-3

 

= 0=3x-7

 

3x=7

 

x = \frac {3}{7}

My Time at the Microsoft Garage and the BCTech Summit

Recently, I got invited to join a pilot program started by Microsoft. It involved working with my peers from my school, and knowledgable mentors at Microsoft. The goal of the program was for the four of us (Me, Sara, Marcus, and Paige) to create a product that we could present at the BCTech Summit, all under our mentor, Stacy Mulcahy. It started off with us brainstorming a number of ideas. We got to play with the tech that they had at Microsoft, and that included 3D printers, Hololenses, and Mixed Reality/Virtual Reality headsets.

While the promise of developing something for virtual reality seemed enticing (And dear god, it really was), we also wanted to create a product that could help people who used it. After taking a day to brainstorm, we wanted to make something that could improve a user’s mental health. We decided to create a smart mirror that would detect the emotion that the user is feeling, and then react and give help on how to deal with that emotion.

 

 

 

 

Over the course of a month and a bit, we came to the Microsoft Garage in our own free time to work on developing the software to detect the users emotion, and the hardware to house everything. I worked on the software with our mentor Stacy Mulcahy. She taught me basic coding with JavaScript, how to add APIs, and how to use Visual Studio and GitHub. Marcus and Paige worked on creating a box to house the mirror. Stacy also ordered some 2-way acrylic panels for us.

The prototype was a taken apart monitor that was connected to a raspberry pi, which is all stored inside of the box. We have a keyboard and mouse connected to the prototype, but later, we would like it to be touch/voice activated. The monitor/pi is stored inside the box, and the two-way acrylic covers the monitor to create the smart mirror functionality. There is also a camera attached to the top of the mirror that scans the person sitting in front of it and sends the face to the API to get it analyzed. Once it’s analyzed, the information gets sent back to the mirror, which is displayed in the ultimate form of millennial communication: an emoji.

We’re super proud of what we created. Being able to proudly walk into the showroom, and talk to all these amazing people in the tech industry about what we built was an amazing feeling.

Pre-Calculus 11 Week 14 – Simplifying Rational Expressions

This week, we started a new unit. This unit is on rational expressions.

A rational expression you might find in grade 11 is \frac{(x+2)(x+3}{(x+2)(x-2)}

To simplify this expression, we find anything common between the numerator and denominator. In this case, the binomial (x+2) exists in the numerator and denominator. So we can cross it out, and our final answer is \frac{(x+3)}{(x-2)}

What if you had quadratics as your numerator and denominator like \frac{x^2+x-6}{(x-2)}

Well, we can factor the quadratic into (x+3) and (x-2). What do you see now? Now our rational expression can be simplified!

\frac{(x+3)(x-2)}{(x-2}

 

(x+3)

 

However, if you have a rational expression like \frac {x+3}{x+2}, remember that this cannot be simplified any further. This is it’s final form! You cannot take away the from the numerator and denominator, as tempting as it is. If you follow through with it, your answers will be wrong. So beware!