Notes for Guestimathon by Lawrence Weinstein
Chapter 1
Take a problem, break into smaller steps s.t. for these steps you can estimate the upperbound and lowerbound immediately. Estimate the smaller steps and multiply it to get an estimate for the eventual answer.
Take the geometric mean of the upperbound and lowerbound. An estimate of the geometric mean is the average of the coefficients and exponents.
Estimate of Geometric mean of
If the sum of exponents is odd, round down and * 3.
Useful Numbers
Common Numbers in Life
# seconds in a year:
# people in the world:
, in developed countries Average computer runs about 3GHz, which is
instructions per second Area of the united states:
. Weights of a Car:
Liquid to Gas: Density expand by 1000.
U.S. per capita gross domestic
product: $85.8kA person drives
per year
Energy
Heat capacity of water is (among the highest of any material in the world)
, Note that 1 cal = 1 J Cost of 1kWh is about
$ Typical energy of a strong chemical bond is
. We know this because common batteries, which convert chemical energy into electrical energy, operate at . It takes one chemical reaction to move one electron through a potential difference of , changing its energy by . Energy Density of Carbon
Energy Density of Gasoline: Density of water:
Cars on average drives
on gasoline, a car usually has 15 gallons (50L), everage cost $3/gal Flushing toilet cost 5L water, 15L/min when showering
incandescent light bulb: 60W - 8 W LED, Candle: 4W. Visible light has a wavelength of between 0.4 and
0.7µmEnergy Efficiency of aircon: about 8. ( for every joule of energy used to run the pump,pumps 3 joules of heat out of the house)
Solar constant: the amount of solar radiation energy received at Earth’s mean distance from the sun
Human
- pupil area:
, minimum flash of light that we can perceive: , wave length of human eye:
Physics
- Outer space is defined as starting at
above the surface of earth