Back-of-the-Envelope Calculations: Scale of the Himalayas
Let's imagine a scale model of the Earth, and let's imagine that the Earth is the size of a basketball. Suppose that you wanted to build the Himalayas to scale on the surface of the basketball. How tall would you make your scale mountains?
About 0.2 mm (less than 1/100"!). The Earth's radius is about 6,400 km (3400 miles). The summit of Mt. Everest rises 8,848 m (29,028') above sea level. Convert meters to kilometers (8.8 km), and compare the height of Everest to the radius of the Earth. The height of Everest is roughly 0.14% of the radius of the Earth. A basketball is about 120 mm in radius. If we find 0.14% of 120 mm, we should have the scale distance of the summit of Everest above the surface of our basketball. If we multiply 120 mm x .0014, we get about 0.2 mm. So, if you wanted to build the Himalayas to scale on the basketball, you would actually have a hard time making them small enough!
References and Resources
This SERC page describes the use of Back of the Envelope Calculations
A View from the Back of the Envelope (more info) : This site has a good number of easy simulations and visualizations of back of the envelope calculations.
The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.