We Must Think Outside the Rocket Equation

The rocket equation contains three variables. Given any two of these, the third becomes cast in stone. Hope, wishing, or tantrums cannot alter this result. Although a momentum balance, these variables can be cast as energies. They are the energy expenditure against gravity (often called delta V or the change in rocket velocity), the energy available in your rocket propellant (often called exhaust velocity or specific impulse), and the propellant mass fraction (how much propellant you need com...

 Plank's Constant

In the year 1900 Max Planck wrote down an equation, E = hv, where E is the energy of a light wave, v is its frequency, and h is a constant which we now call Planck's constant. Planck's equation was the beginning of quantum theory. It said that energy and {22} frequency are the same thing measured in different units. Energy is measured in ergs and frequency in cycles. Planck's constant gives you the rate of exchange for converting frequency into energy, namely, 6 × 10–27 ergs per cycle. B...

 1 = 0.999999999…

This simple equation, which states that the quantity 0.999, followed by an infinite string of nines, is equivalent to one, is the favorite of mathematician Steven Strogatz of Cornell University. "I love how simple it is — everyone understands what it says — yet how provocative it is," Strogatz said. "Many people don't believe it could be true. It's also beautifully balanced. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity."

 Equations are Treasures

Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the treasure-hunt picture of knowledge.