Mathematics
Math this year has been both interesting and challenging. I took honors for both semesters and through this I have done a number of projects. These include creating a poster for a famed mathematician, creating an info graphic on political candidates, and building a corn hole to test probability.
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Freeman Dyson & Project Orion |
My first semester honors project was creating a poster of a famed mathematician. I chose Freeman Dyson for his work and contributions to Project Orion: a nuclear pulse propelled rocket that was tested here in San Diego.
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Election & InfographicsCorn Holes & Probability |
The second project we worked on was the election project. We had to pair up with another student and create infographics on presidential candidates and their statements or actions. The graphic could be predicting their economic views or calculating their impact on the environment or the economy. Our infographic was based on Trump and his economic policy.
Our most recent project was designing and building corn holes to test theoretical and experimental probability. We were paired in groups of two and since I was in honors I was paired with another honors student. Our task was to create a corn hole themed after one of our famous mathematicians. We chose Freeman Dyson and our theme was Project Orion. Our board was going to have two nuclear pulse rockets flying through space.
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Math Concepts
ProbabilityFundamental Counting PrincipleRelative AreaPermutations and CombinationsTree Diagramming"e" and logarithmsThe Law of Large NumbersTheoretical and Experimental Probability |
Probability to put it simply is the number of favorable outcomes over the number of all possible outcomes. This could be pulling out a certain color object out of a mixed bag or throwing a beanbag into a cornhole.
Fundamental Counting Principle states that if one scenario has m possible outcomes and a second independent scenario has n possible outcomes, then there are m * n possible outcomes for the two events to happen together.
Relative area is just the area of a given object.
Permutations
A brief explanation of permutations, think of it like a combination lock ironically. Picking a specific set of values in a specific order from a larger set of other items. Combinations Combinations are simpler, focusing on picking a set of values in no specific order from a larger set of values. Tree diagramming allows us to visualize and draw out every possible outcome of an event and calculate their probabilities. It involves stemming from one outcome and drawing another set of outcomes following that one.
e is Euler's number. The first few digits are 2.718281828. It is an irrational number and is similar in some regards to Pi.
Logarithms represent the power of a number must be raised to in order to produce a desired number. The law of large numbers focuses on the idea that if you test an event enough times the experimental probability will converge with the theoretical probability. (ex. If you toss a coin 1000 times it would be closer to 1/2 than if you tossed it 10 times.)
Theoretical probability is the written probability of a specific event. Experimental probability is the actual outcomes of that specific event when actually tested.
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