100 digits worth memorizing

I was thinking today about how people memorize many digits of , and how it would be much more practical to memorize a moderate amount of numbers to low precision.

So suppose instead of memorizing 100 digits of , you memorized 100 digits of other numbers. What might those numbers be? I decided to take a shot at it. I exclude things that are common knowledge, like multiplication tables up to 12 and familiar constants like the number of hours in a day.

There's some ambiguity over what constitutes a digit. For example, if you say the speed of light is 300,000 km/s, is that one digit? Five digits? My first thought was to count it as one digit, but then what about Avagadro's number 6*10²³? I decided to write numbers in scientific notation, so the speed of light is 2 digits (3e5 km/s) and Avagadro's number is 3 digits (6e23).

Here are 40 numbers worth remembering, with a total of 100 digits.

Powers of 2

2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
2¹⁰ = 1024

Squares

13^2 = 169
14^2 = 196
15^2 = 225

Probability

P(|Z| < 1) 0.68
P(|Z| < 2) 0.95

Here Z is a standard normal random variable.

Music

Middle C 262 Hz
2^7/12 1.5

The second fact says that seven half steps equals one (Pythagorean) fifth.

Mathematical constants

3.14
2 1.41
1/2 0.707
e 2.72
1.62
log_e 10 2.3
log₁₀ e 0.4343
0.577

Here is the golden ratio and is the Euler-Mascheroni constant.

I included 2 and 1/2 because both come up so often.

Similarly, log_e 10 and log₁₀ e are reciprocals, but it's convenient to know both. It may look odd that I report the former to two significant figures and the latter to four. If you're going to memorize 0.43, you might as well memorize 0.4343. Buy two get two free.

Measurements and unit conversion

c = 3e8 m/s
g = 9.8 m/s^2
N_A = 6e23
Earth circumference = 4e7m
1 AU = 1.5e8 km
1 inch = 2.54 cm

Floating point

Maximum double = 1.8e308
Epsilon = 2e-16

These numbers could change from system to system, but they rarely do. See Anatomy of a floating point number.

Decibels

1 dB = 10^0.1 = 1.25
2 dB = 10^0.2 = 1.6
3 dB = 10^0.3 = 2
4 dB = 10^0.4 = 2.5
5 dB = 10^0.5 = 3.2
6 dB = 10^0.6 = 4
7 dB = 10^0.7 = 5
8 dB = 10^0.8 = 6.3
9 db = 10^0.9 = 8

These numbers are handy, even if you don't work with decibels per se.

Update: The next post points out a remarkable pattern between the first and last sets of numbers in this post.

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• Mentally calculate logarithms
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