Math in Nature
This natural sequence appears in sunflower seeds, pinecones, and rabbit populations.
What is the Fibonacci sequence?
Flip a coin twice. What’s the probability of tails?
What is 1/4?
You buy a coffee for $3.50 and pay with a $5 bill. How much change should you get back?
What is $1.50?
Find the next number: 3, 6, 12, 24, …
What is 48?
Solve for y in terms of x:
4x + 2y = 12
What is y = -2x + 6?
A seashell that grows in a spiral often follows this type of curve, related to the golden ratio.
What is a logarithmic spiral?
A bag has 3 red, 2 blue, and 5 green marbles. What is the probability of picking a green marble?
What is 1/2?
A soccer ball is shaped like a sphere with a radius of 11 cm.
What is about 5,575 cubic cm?
Find the next number: 2, 3, 5, 8, 12, 17, …
What is 23?
Factor:
x^2 - 10x+ 16
What is (x - 8)(x -2)?
The shape of a honeycomb is made of this polygon because it uses the least material to hold the most honey.
What is a hexagon?
Roll a fair six-sided die twice. What’s the probability of rolling a sum of 7?
What is 1/6?
A phone originally costs $800. It’s on sale for 15% off, but you also have to pay 8% sales tax. What is the final price of the phone?
What is about $734.40?
Find the next number: 1, 1, 2, 6, 24, 120, …
What is 720?
The sum of two numbers is 21, and one number is twice the other. Find the numbers.
What is 7 and 14?
Snowflakes display this type of symmetry, the same kind often seen in flowers.
What is six-fold or radial symmetry?
The average of 4 numbers is 12. If three of the numbers are 10, 14, and 8, what is the fourth number?
What is 16?
A map uses a scale of 1 inch = 50 miles. If two cities are 4.5 inches apart on the map, how far apart are they in real life?
What is 225 miles?
Find the next number: 1, 4, 9, 16, 25, 36, …
Solve for x: e^(2x) = 7?
What is x = (ln 7) / 2
This branch of math, used to describe natural patterns like clouds, mountains, and coastlines, studies shapes that look similar at different scales.
What is fractals?
What is the probability of opening a 4 combination lock filled with numbers?
What is 1/10000?
A company makes a rectangular shipping box with a square base. The height is twice the side length of the base. If the volume must be 1,728 cubic inches, what is the length of one side of the square base?
What is 12 inches?
Find the sum of the sequence:
2,6,12,20,30,42.
What is 112?
A projectile’s height is given by
h(t) = -16t^2 + 64t + 80.
Find the time it hits the ground.
What is 5 seconds?