Exponential growth: How folding paper can get you to the Moon

Summary

This script explores the concept of exponential growth through the simple act of folding a piece of paper. Starting with a thin sheet of paper, it demonstrates how its thickness doubles with each fold. By folding a paper just 25 times, its thickness reaches nearly a quarter of a mile. The script highlights the astonishing scale of exponential growth, showing how after 30 folds, the paper would be 6.5 miles thick, and after 45 folds, it would reach the Moon. This concept emphasizes how small, repetitive actions can lead to massive results.

Takeaways

• 😀 Folding a piece of paper doubles its thickness with each fold, demonstrating exponential growth.
• 😀 A very fine piece of paper, like Bible paper, is assumed to be 0.001 cm thick for the purpose of this example.
• 😀 After the first fold, the paper's thickness becomes 0.002 cm; after the second fold, it's 0.004 cm, and so on.
• 😀 After 10 folds, the paper reaches a thickness of approximately 1.024 cm (just over 1 cm).
• 😀 After 17 folds, the paper's thickness grows to 131 cm (about 4 feet).
• 😀 With 25 folds, the paper reaches a thickness of 33,554 cm (1,100 feet), about the height of the Empire State Building.
• 😀 Exponential growth becomes evident, with the paper’s thickness increasing dramatically with each fold.
• 😀 If the paper were folded 30 times, its thickness would be 6.5 miles, roughly the average height at which planes fly.
• 😀 After 40 folds, the paper would be 7,000 miles thick, the approximate altitude of GPS satellites.
• 😀 After 45 folds, the paper’s thickness exceeds 250,000 miles, the distance to the Moon, and 46 folds would bring it back to Earth.
• 😀 The concept of exponential growth is highlighted, showing how a small, repeated action can lead to a massive, rapid increase in size or magnitude.

Q & A

How many times can you fold a piece of paper?

In theory, the number of times you can fold a piece of paper is limited by its thickness and size. However, the script explores the concept of folding a very fine paper multiple times and highlights the exponential increase in thickness with each fold.

What is the thickness of the paper after the first fold?

After the first fold, the paper's thickness doubles, making it 2 thousandths of a centimeter, or 0.002 centimeters.

What happens to the thickness of the paper with each additional fold?

With each fold, the thickness of the paper doubles. For example, after the second fold, the thickness becomes 4 thousandths of a centimeter, and this doubling continues with every fold.

What is the thickness of the paper after 10 folds?

After 10 folds, the thickness of the paper reaches 1.024 centimeters, or just over one centimeter.

How thick is the paper after 17 folds?

After 17 folds, the paper would be approximately 131 centimeters thick, or about 4 feet tall.

What is the significance of folding the paper 25 times?

Folding the paper 25 times results in a thickness of about 33,554 centimeters, which is roughly 1,100 feet, making it almost as tall as the Empire State Building.

What is exponential growth, as illustrated by the folding paper example?

Exponential growth refers to the rapid increase in size or quantity where each increase is proportional to the current size. In the case of folding the paper, each fold doubles its thickness, demonstrating exponential growth.

How thick would the paper be after 30 folds?

After 30 folds, the paper's thickness would be approximately 6.5 miles, which is the typical cruising altitude of commercial airplanes.

What happens to the paper's thickness after 40 folds?

After 40 folds, the paper would be around 7,000 miles thick, which is close to the average orbit of GPS satellites around Earth.

How far would the paper reach if folded 45 times?

If the paper were folded 45 times, it would reach the Moon, as the distance from Earth to the Moon is less than 250,000 miles. After 46 folds, it would stretch back to Earth.