Ask Math Anything Topics from March 2020

debbie

3/16/20 Live stream topics

Sum of the terms of the Zeta Fucntion: \( \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... \)
\( \frac{1}{7} \) as a repeating decimal
What's the cube root of \(1\)? (There are three of them!)
Finding roots of quadratic equations by factoring, graphing them in the complex plane
Graphing quadratics like \(x^2, 2x^2, 2x^2 + 1, 2 (x-10)^2 + 1 \)

debbie

3/17/20 Live stream topics

How can we generate true randomness?
The relation of the sides of a triangle whose angles are in an arithmetic progression to the Law of Sines
Side lengths of a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle
Modeling the spread of coronavirus with a graph (each person infects 2 people \( \implies 2 \times 0.8 = 1.6 \)
Why should we study algebra?

debbie

3/18/20 Live stream topics

debbie

Thu 3/19/20 Live stream topics

Simon's Favorite Factoring Trick
Zeno's Paradox
Sum of the terms of the sequence \( \frac{1}{2^1} + \frac{1}{2^2} + \frac{1}{2^3} + \frac{1}{2^4} + \frac{1}{2^5} + \ldots \)
Monty Hall Problem (sort of )
Simplify \( \frac{10}{9997} \)

debbie

Fri 3/20/20 Live stream topics

Golden ratio and how it applies to A4 / A3 paper
Flying around the earth in a plane, and how you can get a triangle with three right angles
Ratios of music notes are nice fractions approaching the golden ratio

debbie

Sat 3/21/20 Live stream topics

debbie

Mon 3/23/20 Live stream topics

Solve \(x^2 - 17x + 72 = 0\) and \(x^2 + 2x + 7 = 0\) using the quadratic method trick
\( 0^0 \) equals what?
\( \frac{1}{0}\) equals what?
Euler's Identity (The "most beautiful equation in math")
\( 0! \) (zero factorial)
Using \( f(n) = \int_{0}^{\infty} x^n e^{-x}dx \) to describe \(0.5\) factorial
The number of diagonals in an \(n\)-sided polygon
Why are there ten digits? (And more about the base-10 system)
Babylonians and how they used base 60
Mental math: \( 19 \times 21\) (Difference of squares)

debbie

Tue 3/24/20 Live stream topics

debbie

Wed 3/25/20 Live stream topics

Business math: investing in different ways
Power of a Point Theorem (geometry)
Troll Paradox
Explain \(e\) using a \(45^{\circ}\)-degree line like \(y = 2^x,\) exponential growth and the slope of \(e^x\)
Is exponential growth like the spread of coronavirus?
How was your first MATHCOUNTS competition?
Fractional exponents
Mental Math: \(16^{1.25}, 16^{1.75}, 2^{0.3}, 5^{0.21},\) and why we can't do this trick with \(7^\pi\)
Do you like science?
Pythagorean Theorem (briefly)
The second most beautiful equation in math
Combustion
Why can xenon form compounds if it is a noble gas?
How to view multiple dimensions
What is the inverse function of an exponential function?
The inverse of \(y = 2^x\) is \(ln_2 \text{ } x\)

debbie

Thu 3/26/20 Live stream topics

How to think about statistics -- look at data and figure out what's the likelihood that something is true underneath it
Probability of flipping a coin twice
World with three types of coins: TT, HT, HH... What is the chance that someone has a certain type of coin given that it flips a H?
Conditional probability: If someone gets HHHHHH, what is the chance that they had HH?
Seeing what happens when we filter out the blue color in the green screen
Surface area of a sphere and its relationship to volume (why is there a factor of 3?)
Volume of a pyramid is \(\frac{1}{3}\) of its bounding box

debbie

Fri 3/27/20 Live stream topics

Negation and reciprocals
Logarithms
Squirting "square rooting"
Exponentiation: \( x \implies 2^x, 5 \implies 32\)
Log (in base 2) of 32 equals 5
Why do people ruin math?
How to find the volume of a green shirt: spray foam all around the shirt and place it in a bathtub (Archimedes and the volume of gold)
Pompeii
Coin flip conundrum (The first person wins if he gets HH; the second person wins if he gets HT. Who wins?)
Which martini glass is half full? (Prof. Loh's favorite paradox.)
Units of density: \( \frac{\text{kg}}{\text{L}}\) Why is there a unit called "cc"? What's the density of water?
What's the volume of the earth? How many time zones are there on Earth?
Fermi problems
Trick for squaring numbers ending in \(5\)
What's the surface area of the Earth?

debbie

Sat 3/28/20 Live stream topics

debbie

Mon 3/30/20 Live stream topics

Delivering papers on a route (Nodes all have an odd number of routes coming out)
Bridges of Konigsberg problem
What class should you take after finishing all high school classes?
How to calculate the mass of the Earth (Fermi problems)
The volume of Earth is \(200\) times \(10^9 \text{m}^3 \)
Mass of the Sun, Mass of the Earth
Use gravity to find the density of the Sun
What are the last three digits of \(43^{100}?\)
How to prepare for the AMC 8
What's the range of \(x^x?\)
How many ways are there to figure out Fibonacci numbers?
Do you like cheese?

debbie

Tue 3/31/20 Live stream topics