December 8, 2019

# XKCD Web Comic #1047: Approximations (described) ## A web comic of romance, sarcasm, math, and language.

(xkcd) Note: ’1 year = pi x 107 seconds’ is popular with physicists. For this
list, I’ve tried to stick to approximations that I noticed on my own.

A Table of Slightly Wrong Equations and Identities Useful for Approximations and/or Trolling Teachers (Found Using a Mix of Trial-and-Error, Mathematica, and Robert Munafo’s Ries tool.) All units are SI MKS unless otherwise noted.

Scene: Three Column Chart

Over first two columns is “Relation:” and over the the third is “Accurate to within:”

 Relations: Accurate to within: One light year (m) 99 to the power of 8 One part in 40 Earth Surface (m to the power of 2) 69 to the power of 8 One part in 130 Ocean’s volume (m to the power of 2) 9 to the power of 19 One part in 70 Seconds in a year 75 to the power of 4 One part in 400 Seconds in a year (Rent method) 525,600 times 60 One part in 1400 Age of the Universe (seconds) 15 to the power of 15 One part in 70 Planck’s Constant 1/(30 to the power of (pi to the power of e)) One part in 110 Fine Structure Constant 1/140 [I’ve had enough of this 137 crap] Fundamental Charge 3/(14 times (pi to the power of (pi to the power of pi)) White House Switch Board 1/(e to the power of(the pi root of (1 + (the e-1 root of 8)))) Jenny’s Constant (7 to the power of ((e/1)-(1/e)) – 9) times pi to the power of 2 Intermission:World Population Estimate which should stay current for a decade of two: Take the last two digits of the current year (example: “2014” with a square drawn around the “14”. An arrow runs from that arrow down to another square with “14” in it.). Subtract the number of leap years since Hurricane Katrina. (An arrow runs from the “14” square to a new square with “12” in it. Next to that square are “2008” and “2012” stacked and an arrow running from them to the arrow between the “14” and the “12” square.) Add a decimal point. (An arrow runs from the “12” square to a new square with “1.2” in it.) Add 6. (An arrow runs from the “1.2” square to a new “1.2” square with a “6 +” to the right. To the left is an equal sign and a square with “7.2” in it.) Next to that square is “World Population in Billions.” (Next to all of that is a gray version) Version for US Population: “2014” with a square drawn around the “14.” An arrow runs to a box with “subtract 10” in it. An arrow runs to another square with the resultant “4” in it. An arrow runs to the instruction “Multiply by 3” and an arrow runs from that to a square with the product, “12,” in it. An arrow runs from that to a box with “Add 10” in it and an arrow runs from that up to a square with the result, “22,” in it. To the right of that square is a “3” and to the left is the word “Million.” Electron Rest Energy (e/7 to the power of 16) times J One part in 1000 Light-year (miles) 2 to the power of 42.42 One part in 1000 Sin(60 degrees) = (square root of 3)/2 =e/pi One part in 1000 Square root of 3 = (2 times e/pi) One part in 1000 Gamma (Euler’s Gamma Constant) 1/(square root of 3) One part in 4000 Feet in a meter 5/(the e root of pi) One part in 4000 Square root of 5 = (2/3 + 3/2) One part in 7000 Avogadro’s Number 69 to the power of (pi to the power of (the square root of 5)) One part in 25,000 Gravitational Constant G 1/(e to the power of (pi-1 to the power of (pi +1))) One part in 50,000 R (Gas Constant) (e +1) (square root of 5) One part in 50,000 Liters in a Gallon 3 + (pi/4) One part in 500,000 g 6 + ln(45) One part in 750,000 Proton-Electron Mass Ratio ((e to the power of 8 ) – 10)/ Phi One part in 5,000,000 Ruby laser wavelength 1/(1200 to the power of 2) [Within actual variation] Mean Earth Radius (5 to the power of 8 ) * 6 * e [Within actual variation] Protip—Not all of these are Wrong: Square root of 2 = (3/5) – (pi/(7-pi)) Cos(pi/7) + Cos3(pi/7) + Cos(5pi/7) = 1/2 (Euler’s Gamma Constant) Gamma =(e/(3 to the power of 4) + (e/5)) Square root of 5 = (13 + 4pi)/(24-4pi) Sigma (1/n to the power of n) = ln(3) to the power of 3

Hover text: Two tips: 1) 8675309 is not just prime, it’s a twin prime, and 2) if you ever find yourself raising log(anything) to the power of e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong.

Warning: This comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors). Comic by xkcd.com. Described by BlindGadget under the Creative Commons license.