Methods for Approximating Pi

Casey from the AP periodical leads a group of mathematicians in a challenge to approximate the value of Pi using various unconventional methods without calculators. Participants employ techniques such as drawing polygons, using pendulums, Buffon's Needle, balloon volumes, and the spigot algorithm. Each method is explained and tested, with results compared to determine the closest approximation to Pi. The challenge concludes with Buffon's Needle method achieving the closest value.

What is the main objective of the Pi approximation challenge?

• To calculate Pi using calculators

• To find the exact value of Pi

• To approximate Pi using various methods without calculators

• To compare different mathematical constants

What method does Sam use to approximate Pi?

• Using a pendulum

• Blowing up balloons

• Drawing polygons with increasing sides

• Dropping straws on paper

How does Paul plan to calculate Pi using a pendulum?

• By measuring the circumference of a circle

• By timing the pendulum's complete swing

• By counting the number of swings

• By using a digital stopwatch

What is the principle behind Buffon's needle method?

• Blowing up balloons to measure volume

• Dropping straws to calculate probability

• Using pendulums to measure time

• Using polygons to approximate Pi

What unique method is used to approximate Pi with cartwheels?

• Measuring the diameter of a circle

• Counting the number of rotations

• Using the landing point of a foot

• Timing the duration of a cartwheel

How does Andrew use balloons to approximate Pi?

• By counting the number of balloons

• By timing the inflation

• By calculating the volume of water

• By measuring the circumference

What is the basis of the formula involving prime numbers?

• Using odd numbers

• Using even numbers

• Using Fibonacci sequence

• Using successive prime numbers

What algorithm does Ash use for calculating Pi?

• Euler's algorithm

• Spigot algorithm

• Buffon's needle

• Newton's method

What was a significant source of error in Paul's pendulum method?

• The timing of the swings

• The weight of the pendulum

• The accuracy of the stopwatch

• The length of the string

Which method achieved the closest approximation to Pi?

• Paul's pendulum method

• Buffon's needle method

• Andrew's balloon method

• Sam's polygon method