Mathematical modeling using proportionality

(Math Modeling Lecture 2.3) In this lesson, we explore the use of proportionality in mathematical modeling. This concept is illustrated through various examples, including

- Hooke's Law in physics, which relates the restoring force of a spring to its displacement.
- The relationship between drag force and velocity in free fall, like skydiving.
- How Eratosthenes estimated the circumference of the Earth using geometry and shadows
- Kepler's Third Law, relating the square of a planet's orbital period to the cube of its average distance from the Sun.
- The geometric reasoning behind small cell sizes, tying in the relationship between surface area and volume in biology.

The discussion concludes with a look at heartbeat data in mammals, where the heart rate is inversely proportional to the mass to the one-third power (this is version 1 of our analysis of this data). We use MATLAB to analyze this relationship, excluding outliers like bats, and fit a line of best fit to the data.

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