Mathematical Thinking

Table of Contents
Introduction
Fermi's Piano Tuner Problem
How Old is Old?
If the Terrestrial Poles were to Melt...
Sunlight Exerts Pressure
Falling Eastward
What if an Asteroid Hit the Earth
Using a Jeep to Estimate the Energy in Gasoline
How do Police Radars really work?
How "Fast" is the Speed of Light?
How Long is a Light Year?
How Big is a Trillion?
"Seeing" the Earth, Moon, and Sun to Scale
Of Stars and Drops of Water
If I Were to Build a Model of the Cosmos...
A Number Trick
Designing a High Altitude Balloon
Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water
Calendar Calculations
Telling Time by the Stars - Sidereal Time
Fields, an Heuristic Approach
The Irrationality of
The Irrationality of
The Number (i)i
Estimating the Temperature of a Flat Plate in Low Earth Orbit
Proving that (p)1/n is Irrational when p is a Prime and n>1
The Transcendentality of
Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions
Maxwell's Equations: The Vector and Scalar Potentials
A Possible Scalar Term Describing Energy Density in the Gravitational Field
A Proposed Relativistic, Thermodynamic Four-Vector
Motivational Argument for the Expression-eix=cosx+isinx
Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics


How Big is a Trillion?

In the U.S., one trillion is written as the number "1" followed by 12 zeros (1,000,000,000,000). One year of clock time =

(60sec/min) x (60 min/hr) x (24 hr/da) x (365.25 da) = 3.16 x 107 sec

One trillion seconds of ordinary clock time =

( 1012 sec)/( 3.16 x 107 sec/yr) = 31,546 years!

Six trillion seconds equals 189,276 years. Now, as an aside, along with the nearly six trillion miles in the light-year, you might be interested to know that there are nearly five trillion dollars in the current U.S. national debt. Is it any wonder that our politicians in Washington are concerned?

(An interesting bit of trivia: If one were to count the national Debt at the rate of one dollar per second, he or she would have to use a mechanical counter to click off the digits. Why? Because, if he or she counted in the usual way, saying "one, two, three, …" etc., there would be numbers whose names are so large, that it would take more than a second of clock time to pronounce them. For example: "Nine hundred and ninety nine billion, nine hundred and ninety nine million, nine hundred and ninety nine thousand, nine hundred and ninety nine," takes about 8 seconds to pronounce.)