3023: The Maritime Approximation

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The Maritime Approximation

Title text: It works because a nautical mile is based on a degree of latitude, and the Earth (e) is a circle.

Explanation

This explanation may be incomplete or incorrect: Created by a SEMICIRCULAR SAILOR - Please change this comment when editing this page. Needs explanation of the origins of the units and constants involved for readers to investigate the coincidentality of the relationship. Do NOT delete this tag too soon. If you can address this issue, please edit the page! Thanks.

Mph, or miles per hour, and knots are both units used to calculate the speed of vehicles. Miles per hour are typically used in the US 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, however Randall has humorously noticed that π mph = e knots. This is a coincidence^{[citation needed]} despite the claim of the title text, 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. Randall has made similar observations of different dimensions that equal each other in the past in the past with comics such as 687: Dimensional Analysis, where he compares 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 "miliJupiters," 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.

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

1. The mile per hour (mph) is a unit of speed common for motor vehicles in a few countries, such as the United States and United Kingdom.
2. The knot is a unit of speed that is one nautical mile (1 852 m) per hour, used in nautical contexts.
3. π is a number equal to the ratio of a circle's circumference to its diameter, about 3.14159.
4. 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) ≈ 2.72996 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 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 but indeed, being easy to remember is all it has going for it. Otherwise 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.

Transcript

This transcript is incomplete. Please help editing it! Thanks.

[Equation inside a frame with a footnote:]

π mph = e knots*

*Correct to <0.5%

[Caption below the panel:]

The sailor's version of e^iπ=−1

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Discussion

1.609*3.1416926 looks like 1.852*2.718281828 seems legit 172.71.124.233 (talk) 21:37, 11 December 2024 (UTC) (please sign your comments with ~~~~)

I added the basics of an explanation, it definitely needs some work, but it should do as a starting point. Hope I did well! 172.68.22.92 23:06, 11 December 2024 (UTC)

The knot is exactly 1 nautical mile per hour. Meanwhile π/e ≈ 1.155727, which is close to nm/mi = kt/mph ≈ 1.15078 172.70.134.135 23:26, 11 December 2024 (UTC)

This article says one knot is 1.2 MPH, which is true for the number of digits of precision stated. But in context of the claimed precision of 0.5% it would be more helpful to state that one knot is approximately 1.151 MPH. https://en.wikipedia.org/wiki/Knot_(unit) 172.71.159.7 00:08, 12 December 2024 (UTC)

Transcendental : relating to a spiritual realm. eg "the transcendental importance of each person's soul". Works for me. 162.158.186.248 (talk) 00:09, 12 December 2024 (UTC) (please sign your comments with ~~~~)

Just as a fun fact, "transcendental" in this case is referring to Transcendental number, which are numbers that cannot be expressed as the root of a polynomial, which basically means they cannot be found using algebra alone. I think the two definitions are related, since these numbers "trancend" the "realm" of numbers which can be found with algebra. 172.68.22.82 01:04, 12 December 2024 (UTC)

Another maritime approximation: 1 meter/sec nearly equals 2 knots (actual is 1.94384), perhaps there is an actual explanation for this?

A better mnemonic, which I actually use: miles→km is Fibonacci. 2miles≈3km, 3miles≈5km, 5miles≈8km, 8miles≈13km, 13miles≈21km, 21miles≈34km, 34miles≈55km, 55miles≈89km, 89miles≈143.23km, Fibonacchi would predict 144km. But at that point, you can just remove some less significant digits anyway. For everything in between, you can estimate how far it is from the nearest Fibonacci numbers, that works pretty well, too. Fabian42 (talk) 01:54, 12 December 2024 (UTC)