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


Of Stars and Drops of Water

Moving outward from the solar system: The next closest star to Earth beyond the sun is Proxima Centauri, at a distance of 4.3 light-years (i.e., 4.3 x 6 trillion miles). It is one among billions in our galaxy, the Milky Way. The Milky Way is a pinwheel of stars 2,000 light-years "thick", and 100,000 light-years in diameter. It holds over a hundred-billion (one followed by 11 zeros) stars. The next closest spiral galaxy is M31 in the constellation Andromeda. It is nearly 2 million light-years away (12 million-trillion or 1.2 x 1013 miles). M31 is near the limit of naked eye visibility. The Hubble telescope extends the limit of visibility out to 10 billion (10,000,000,000) light-years. From Hubble, we estimate that there are about 50 billion (50,000,000,000) galaxies in the observable universe! And if each galaxy contains a hundred-billion stars, then the observable universe contains 5,000,000,000,000,000,000,000 ("5" followed by 21 zeros or five "sextillion") stars. By contrast, a cube of water, one inch on a side, contains about 600,000,000,000,000,000,000,000 ("6" followed by 23 zeros, or six-hundred sextillion) molecules! There are 120 times more water molecules in the cubic inch of water than there are stars in the observable universe!!!