Nick's AQR Portfolio

Unit 1

Networks: Circuits and Paths

In Unit 1 we looked at connected graphs and how to figure out if they have Euler paths or circuits. An Euler path travels through every edge in a graph exactly once, and an Euler circuit does the same but loops back to where you started. We also covered Hamilton paths and circuits which are a bit different since those require visiting every vertex exactly once instead of every edge. A big part of the unit was seeing how these ideas actually show up in real life situations like routing and scheduling problems.

Sum of Degrees = 2 × Number of Edges

Euler Path / Circuit

Uses every edge exactly once
0 odd vertices: Circuit
2 odd vertices: Path
4+ odd vertices: Neither

Hamilton Path / Circuit

Visits every vertex exactly once
Doesn't need to use every edge
Circuit means you return to start
Good for finding shortest routes

Page 1

Page 2

Page 3

Page 1: Euler Circuits (01 Evaluate)

Page 2: Circuits Application Quiz

Page 3: Circuits Paths Practice Quiz

Google Maps and Graph Theory

Google Maps is a good real life example of graph theory because every location is basically a vertex and every road between them is an edge with a weight representing distance or time. When you put in multiple stops it finds the most efficient route to hit all of them, which is pretty much the same thing as a Hamilton path. It picks the shortest way to get everywhere without having to backtrack or repeat roads.

Unit 2

Measurement, Data, and Real-World Math

Unit 2 Summary

Unit 2 covered a lot of different math topics that all connect to how we measure and estimate things in the real world. We worked with aspect ratios to understand how widescreen movies fit on a TV and how tires affect your actual speed and odometer reading. We also learned about weighted averages and the consumer price index to see how averages work when not everything counts equally. On top of that we practiced estimating large numbers, like figuring out how many M&Ms fit in a container, which taught me how to break a big problem into steps instead of just guessing.

Graded Assignment 06 Worksheet

Unit 02 – Lesson 04 · AQR A · UT High School

Interactive Notebook Pages

Selected pages from my Unit 2 interactive notebook

Notebook page 1 - Estimating Large Numbers

Notebook page 2 - M&M container estimation

Notebook page 4 - Aspect ratios and golden ratio

Real Life Example: Changing Tire Sizes on a Car

One thing we did in Unit 2 was work out what happens to your speedometer when you put bigger tires on a car. We used a Corvette example where the factory tires were P245/40R18 and the new ones were P285/35R19. The new tires have a bigger circumference, so every rotation moves the car further than the original tires would. The car's computer is still counting rotations based on the old tire size, so the odometer and speedometer both read lower than reality. The math showed that if your speedometer says 80 mph you are actually going about 83.5 mph, and if the odometer reads 8,000 miles you have actually driven about 8,346. I thought that was really interesting because it is something that actually matters if you are trying to stay under the speed limit or track your real mileage.

      If the speedometer reads 80 mph with the new tires, the actual speed is 80 x (84.3 / 80.8) = about 83.5 mph. The same scale factor applies to the odometer: 8,000 x 1.0433 = 8,346 miles actually driven.
    