Mildly On-Topic: Converting Miles to KM using the Fibonacci Sequence

[MattTuck]

Blatantly stole this from reddit, but cyclists probably have more need to convert KMs to Miles than most, so I thought it should be here also. And most of you guys are nerds.

https://www.reddit.com/r/LifeProTips...p_you_quickly/

The Fibonacci sequence is a series of numbers where every new number is the sum of the two previous ones in the series.

1, 1, 2, 3, 5, 8, 13, 21, etc.
The next number would be 13 + 21 = 34.

Here's the thing: 5 mi = 8 km. 8 mi = 13 km. 13 mi = 21 km, and so on.

Edit: You can also do this with multiples of these numbers (e.g. 5*10 = 8*10, 50 mi = 80 km). If you've got an odd number that doesn't fit in the sequence, you can also just round to the nearest Fibonacci number and compensate for this in the answer. E.g. 70 mi ≈ 80 mi. 80 mi = 130 km. Subtract a small value like 15 km to compensate for the rounding, and the end result is 115 km.

This works because the Fibonacci sequence increases following the golden ratio (1:1.618). The ratio between miles and km is 1:1.609, or very, very close to the golden ratio. Hence, the Fibonacci sequence provides very good approximations when converting between km and miles.

[ColonelJLloyd]

Well, look at that. Thanks!

[false_Aest]

All you need to know:

100k ~ 60 miles (and 10k ~ 6 miles)
40k ~ 24 miles
32k ~ 20 miles

[mistermo]

I intend to google the "golden ratio". But am curious about what it is and how it's used.

[marciero]

Originally Posted by false_Aest

All you need to know:

100k ~ 60 miles (and 10k ~ 6 miles)
40k ~ 24 miles
32k ~ 20 miles

I think you are missing the point here.

[marciero]

Originally Posted by mistermo

I intend to google the "golden ratio". But am curious about what it is and how it's used.

As I'm sure you've found, it is an irrational number (cant be expressed as p/q with p and q whole numbers) that turns up in all kinds of seemingly unrelated areas in math, sciences, and natural phenomena.

Incidentally, there is a formula for the nth number in the sequence, so, for example, you can find it without recursively finding all the preceding numbers in the sequence. You cant do it in your head (say, while riding) though. But as I indicated, I dont think the point here is to use this to actually do conversions.

[Llewellyn]

Why on earth would you want to convert kilometres into an archaic measurement like miles

[stephenmarklay]

Neato. This will give us something to play with on our trip to Canada. My daughter will eat this up.

[nooneline]

A minor edit to the quote in the OP. The Fibonacci Sequence doesn't increase based on the golden ratio... the ratio of n+1 to n approaches the Golden Ratio as the sequence approaches infinity. Since, obviously 2:1 =/ 1.6108, likewise neither does 5:3. The bigger the pair of Fibonacci neighbors, the closer to 1.6108... the ratio is.

My wife, a mathematician (aka math doctor) has shown me some really surprising and cool puzzles where the Fibonacci Sequence rears its head. It's crazy and mindblowing to see the many different phenomena in different fields that can be described by the Fibonacci Sequence.

[Black Dog]

Originally Posted by Llewellyn

Why on earth would you want to convert kilometres into an archaic measurement like miles

Exactly. Why not measure in furlongs, thumbs, cubits, or rods... Metric rules...see what I did there?

[Duende]

Love this! Thx MattTuck!

[thunderworks]

Originally Posted by mistermo

I intend to google the "golden ratio". But am curious about what it is and how it's used.

In Western architecture, the Golden Rectangle, based on the 1:1.6 golden ratio relationship, underpins much design. The Greek buildings of antiquity were mostly built using the ratio, where the long side of a structure was 1.6X the short side. The fundamental relationship was adopted by the Romans, and even now, much Western design uses that ratio as a spatial building block.

I'm a furniture maker, and frequently use that ratio as the beginning point of a design. I don't always end up there, but usually consider it during the design phase.

[Cicli]

I measure my rides in "smiles per mile" and it dosent work in metric. Smiles per kilometer sounds dumb.