Talk:3023: The Maritime Approximation
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? 162.158.155.117 (talk) 01:36, 12 December 2024 (UTC) (please sign your comments with ~~~~)
- Both the nautical mile and meter derive from measurements of the Earth's circumference, and the number of seconds in an hour is related to the base-60 counting system (as is the number of degrees in a circle), but beyond that it's just how the math works out. 1 nautical mile is (well, was) 1/60 of a degree of latitude. 1 meter is (was) 1/10,000,000 of the distance from the Equator to the North Pole, which is 90°, so that's 9/1,000,000 of a degree of latitude. So 1 m = 27/50,000 nmi. Then, an hour is 3600 s. So 1 m/s = 27∙3600/50,000 nmi/hr. Cancelling, that's 1 m/s = 243/125 nmi/hr, and that fraction is quite close to 2. But there's no real deeper connection.172.70.115.102 15:08, 12 December 2024 (UTC)
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)
- Yes, similar to this comic the ratio of km to miles (1.6093) is very close to the golden ratio (1.6180) or (1 + sqrt(5))/2. 172.68.54.64 04:28, 12 December 2024 (UTC)
My favorite one is that pi squared is approximately the acceleration of gravity (9.8 m/s^2). The best part is that is NOT a coincidence. 172.71.183.174 06:11, 12 December 2024 (UTC)
- How is this not a coincidence? (Wowitschris (talk) 20:56, 12 December 2024 (UTC))
- It's actually a coincidence, but in a weird sense it almost would not be. When French revolutionaries invented the metric system, they considered defining the meter as the length of a pendulum with a period of one second. If they had done that, g would be exactly pi squared. But it was already known back then that g varies with location, so the actual definition based on earth's circumference was adopted --141.101.105.87 06:39, 13 December 2024 (UTC)
Actually the most common form of Euler's identity is eiπ + 1 = 0; I find it odd that Randall never writes it that way (see 179 and 2492 for example). --172.69.68.4 12:47, 12 December 2024 (UTC)
- The form that you wrote and Randal's preferred form are identical. The equations are slightly different, but they are the same form. Other forms would involve using trigonometric functions, infinite series, integrals or ... something else. Galeindfal (talk) 18:38, 12 December 2024 (UTC)
- If you don't like calling it "form" say "appearance" or "arrangement"... anyway the most common is eiπ + 1 = 0 because it includes the three main operations and 5 fundamental constants, so it is usually regarded as aestetically more satisfying.
- --172.71.114.137 12:01, 13 December 2024 (UTC)
