Date modified: Thu 2023-08-10 . 10:55 AM
Date created: Sat 2023-10-07 . 09:02 PM
# Week 1 Thursday: On geometry and calculus. In class today we discussed the worksheet "Size of Earth", here's a summary: When approach problems, here are some good things to try: 1. Collect information and draw relevant diagrams 2. Label all known quantities and unknowns 3. Find relations among the quantities 4. State your assumptions: The assumptions that we make may alter the problem, but may also simplify the problem. We discussed the following: 1. What is $\pi$ and what is a radian measure for angle. 2. How to come up with the arclength formula ourselves, using what the definition of radian angle measure is. 3. Alternating interior angles of a transversal line cutting through two parallel lines. 4. Why is $\arctan\left( \frac{1}{8} \right)=0.12435...$ so close to $\frac{1}{8}=0.125$ ? 5. Graph of $\arctan(x)$ near $x=0$, and its tangent line at $x=0$. 6. The tangent line is a "good" approximation of the graph of function near the point of tangency.