Hacker News Reader

Comment by numbergeek666 | Hacker News Reader

open google earth use ruler for below

miles from Angkor Wat to Giza pyramid 4754 miles. This multiplied by the glden ratio of 1.618 give 7692 miles which is the distance from Giza to Nazca . Now 7692 miles multiplied by the golden ratio again gives 12446, which is the distance from Nazca to Angkor Wat

why?

View on HN

Because our brain is a superb pattern matcher. It can see pattern almost everywhere, even when there are none. That has helped our ancestors find animals that can be hunted, and prepare for flooding events timed at certain intervals (12 full moons until the next harvest/sowing season). But that also leads to situations where coincidental patterns are found, where the constituent parts have no casual relationship to one another.

I bet you can find even more patterns, where there are none: http://www.tylervigen.com/spurious-correlations

It’s called ‘coincidence’: you have so many sites (N) to choose from, and there are N²︎ connections between them. To some degree of accuracy you’re going to find ratios between some of these that are ‘close’ to apparently ‘important’ numbers (and there’s plenty of those, and of course integer multiples thereof, which seem to catch just as much attention).

It’s just a numbers game (excuse the pun). It’s just pure numerology. And an overabundance of ratios and constants and multiples thereof to choose from. It would be pretty unlikely that no such coincidental values would turn up.

In this case, it's all about how triangles behave on a unit sphere, if one edge gets close to the length of π, or half a circumference. For Earth and Miles, r is 3963 and r * π = 12450, which is awfully close to 12446.

We are effectively looking at a https://en.wikipedia.org/wiki/Spherical_lune here. The dihedral angle can be chosen freely. One half great circle is going directly between the antipodal points, while the other half great circle is intersected at the ratio into two edges.

So all you need to find are two antipodal points. Then any point lying on the two "small" circles defined by the ratio in either direction of the half great circle fullfills this condition. Helpful if you have bit of wiggle room with a place like Nazca.

If we take for simplicity the North and South Pole then any point at the latitude 21.25 North or South would fullfill this condition. Mecca at 21.4N would come within 15 km of that band already.

Oh boy: https://www.goldennumber.net/golden-ratio-of-earth/

Pleased to make your acquaintance, geometer! I’m of the algebraic faction myself. I bid you a pleasant day.

The distance from Angkor Wat to Giza is: 4754 miles. And the distance from Gize to Nazca is: 4754 x φ miles.

By adding these, you get that the distance from Angkor Wat to Nazca is 4754 (1+φ) miles.

But φ is defined such that 1+φ = φ², [Verify for yourself that 1.61803398875² = 2.61803398875]

So thus, the distance from Ankor Wat to Nazca can also be described as 4754 φ² miles.

Also were talking spheroid surface distances aka geodesics here. So unless three places lie on a great circle their distances are not cummutative, since they form a geodesic triangle.

Google Earth Engine's geometry constructors build geodesic geometries by default

https://developers.google.com/earth-engine/geometries_planar...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, the geodesics are great circles (like the equator). The geodesics in a space depend on the Riemannian metric, which affects the notions of distance and acceleration

Reply on news.ycombinator.com