Using Fibonacci numbers to convert from miles to kilometers and vice versa

Original Article ↗ Hacker News Discussion ↗

Fibonacci-based conversion trick

  • Thread discusses using Fibonacci numbers for rough miles↔kilometers and kg↔lbs conversions, leveraging that consecutive Fibonacci ratios approach the golden ratio.
  • Some find it delightful, memorable, and “bar trick” material; others view it as mainly an entertaining curiosity.
  • A few point out related facts: Binet’s formula, golden ratio definition, and links to Lucas sequences.

Practicality vs over-engineering

  • Several commenters question practicality: expressing arbitrary numbers as Fibonacci sums is slower than just multiplying by ~1.6 or 0.6.
  • It’s often framed as “Rube Goldberg” or over-engineered compared to simple fractions.
  • Others defend it as “math art” or a thinking aid: not optimal, but fun and occasionally useful for small, common values (e.g., speed limits).

Alternative mental conversion methods

  • Common simple heuristics:
    • Multiply miles by 8/5 or 1.6; km by 5/8, 3/2, or 2/3 when “close enough” is fine.
    • Remember anchor points like 100 km ≈ 62 mph; 10 km ≈ 6 mph; 1 mile ≈ 1.6 km.
    • Use percentage-based tricks: +60% for miles→km; for pounds→kg “halve then subtract 10%”.
    • Speed-limit-specific tricks: multiples of 5 or 10, or using 16/10 via repeated doubling/halving.
  • Many argue these are faster, more accurate, and require less memorization than Fibonacci decompositions.

Golden ratio and unit-history discussion

  • Consensus in the thread: similarity between mile–km ratio and golden ratio is coincidental.
  • Some provide historical/contextual details on the mile, meter, and kilometer definitions and note other numerical near-coincidences (e.g., π² ≈ g, pendulum-period approximations).

Zeckendorf theorem and number theory side-notes

  • Zeckendorf’s theorem is cited to justify representing any integer as a sum of Fibonacci numbers.
  • Commenters discuss uniqueness, non-consecutive constraints, and show simple greedy decompositions.
  • Some note this adds conceptual interest but not practical benefit for conversions.

Tools, slide rules, and other systems

  • References to slide rules and circular slide rules for mental/analog calculation, including currency conversions.
  • Mentions of browser extensions and exact inch–cm definition enabling precise imperial↔metric threading on lathes.

Meta: blog quality and tone debate

  • Significant subthread criticizes the linked site’s “spammy” SEO, subscription tools, and security claims.
  • Others push back, calling this unhelpful negativity and arguing to focus on the mathematical content.