Editing 3023: The Maritime Approximation

{{comic
| number    = 3023
| date      = December 11, 2024
| title     = The Maritime Approximation
| image     = the_maritime_approximation_2x.png
| imagesize = 265x126px
| noexpand  = true
| titletext = It works because a nautical mile is based on a degree of latitude, and the Earth (e) is a circle.
}}

==Explanation==
{{incomplete|Created by a SEMICIRCULAR SAILOR - Needs explanation of the origins of the units and constants involved for readers to investigate the confidentiality of the relationship. Also, needs clear explanation of title text. Do NOT delete this tag too soon.}}
Mph ({{w|miles per hour}}) and {{w|Knot (unit)|knot}}s (''nautical miles'' per hour) are both units used to calculate the speed of vehicles. Miles per hour are typically used in the {{w|Miles per hour|US, UK and some smaller countries}} for the speed of cars and other similar vehicles, while knots are used by some sailors or pilots to describe the speed of ships or aircraft. Novice sailors or sailors who spend a lot of time on land may find it helpful to quickly convert between mph and knots. Usually, this is the form of 1 knot = 1.2 mph, or 1 mph = 0.87 knots (1.85 km/h and 0.54 knots for metric sailors), however [[Randall]] has humorously noticed that π mph ≈ e knots: π mph = [https://www.google.com/search?client=firefox-b-d&q=pi+mph+in+knots 2.72997] knots, {{w|E_(mathematical_constant)|e}} =  2.71828. Despite the claim of the title text, this is a coincidence,{{Citation needed}} since even though knots are based on nautical miles, which are related to degrees of latitude (and thus to π, which is used to describe the circumference of a circle), miles per hour have no relation to either e or π. Furthermore, the title text makes the connection to e by mentioning "Earth (e)" but e is not a commonly used symbol or abbreviation for Earth and even if it were, it has nothing to do with Euler's number e. The Earth is also not a circle.

The equality shown in this strip consists of several different parts:

# The mile (1609.344 m) per hour (mph) is a unit of speed common for motor vehicles in a few countries, such as the United States and United Kingdom.
# The knot is a unit of speed that is one nautical mile (1 852 m) per hour, used in nautical contexts.
# π is a number equal to the ratio of a circle's circumference to its diameter, about 3.14159.
# e is Euler's number, the base of the natural logarithm, about 2.71828.

π mph × (1609.344 meters/statute mile ÷ 1852 meters/nautical mile) ≈ 2.729969 knots. The result is only about 0.43% larger than ''e'' knots ≈ 2.71828 knots.

The joke is that it is not exact, but only correct to a certain percentage, unlike {{w|Euler's Identity}}, which is exact, and that's what makes the latter truly remarkable. It isn't helped by the fact that it carries the implication that this neat, easy to remember identity is actual useful for sailors, when really being easy to remember is all it has going for it: it doesn't make calculations any easier and is impossible to do without a calculator or paper, and doing it on paper is much harder than other conversions, given that Pi and e are both irrational, and transcendental.

Knots are related to the circumference of the Earth, which can introduce pi, but this is only "useful" if you want to express your speed as a fraction of the radius of earth: 1 knot = 1 nautical mile per hour = 1/60 of a degree of Earth's circumference per hour = 1/21,600 of Earth's circumference per hour = 2π/21,600 x Earth's radius per hour. However, nowadays this is an approximation, because a nautical mile is defined as exactly 1852 m, which is not exactly 1/60 of a degree of Earth's circumference.

Randall has made similar observations of different dimensions that equal each other in the past with comics such as [[687: Dimensional Analysis]], where he compares {{w|Planck Energy}}, the pressure at the earth's core, the gas mileage in a Prius, and the width of the English Channel to Pi. In addition, in [[What If?]], he has compared the mass of Earth to be Pi "milliJupiters," or Pi times the mass of Jupiter divided by 1000, and noted that the volume of a cube with side lengths of one mile is roughly similar to the volume of a sphere with a radius of 1 kilometer. In [[1047: Approximations]], Randall gives a lot of other similar approximations.

==Transcript==
:[In a small panel an equation is shown. There is a footnote below the equation:]
:<big>π mph = ''e'' knots*</big>
:<small>*Correct to <0.5%</small>

:[Caption below the panel:]
:The sailor's version of e<sup>iπ</sup>=−1

{{comic discussion}}

[[Category:Math]]