Telugu (a language of southern India) has an interesting traditional numeric system: base ten for integers, and base four for fractions.
U+0C78 "౸" TELUGU FRACTION DIGIT ZERO FOR ODD POWERS OF FOUR
U+0C79 "౹" TELUGU FRACTION DIGIT ONE FOR ODD POWERS OF FOUR
U+0C7A "౺" TELUGU FRACTION DIGIT TWO FOR ODD POWERS OF FOUR
U+0C7B "౻" TELUGU FRACTION DIGIT THREE FOR ODD POWERS OF FOUR
(U+0C66 "౦" TELUGU DIGIT ZERO is used for even powers of four too)
U+0C7C "౼" TELUGU FRACTION DIGIT ONE FOR EVEN POWERS OF FOUR
U+0C7D "౽" TELUGU FRACTION DIGIT TWO FOR EVEN POWERS OF FOUR
U+0C7E "౾" TELUGU FRACTION DIGIT THREE FOR EVEN POWERS OF FOUR
Few Telugu speakers even know about this any more—no one can read even the traditional integers (౦౧౨౩౪౫౬౭౮౯), because 0123456789 have replaced them. (This is the case in most but not all Indian languages. Bengali’s traditional digits are still common, so you can enjoy ৪ being four and ৭ seven.)
A couple of articles and discussions about it:
• https://www.unicode.org/wg2/docs/n3156.pdf is the best public resource I know of (Unicode proposals and related papers are often delightful for information on obscure written stuff, because they had to write down and publish the details to get the characters encoded). One tid-bit: NYSE used a similar decimal/quaternary system until early 2001.
• https://blog.plover.com/math/telugu.html from the same site as the current article, discussed in https://news.ycombinator.com/item?id=14683767 nine years ago.
Prior to decimal pricing, us exchanges priced in eighths. An article [1] I found from a source I don't recognize says that there was briefly trading in sixteenths, but I guess I wasn't following the stock markets that closely then and I missed it.
https://tontinecoffeehouse.com/2018/11/05/pricing-in-eighths...
If they do consistently that is not too bad. Compare that with imperial units, which, depending on the quantity and sometimes its magnitude, uses
- base 10 for integers and base 12 for fractions (lengths in feet and inches). Alternatively, base 10 for mikes, base 5,280 for feet’s in a mile, base 12 for inches in a foot.
- base 10 for integers and base 14 for fractions (weights in stone and pound). Alternatively, there’s a base 112 when measuring in long tons and stones or 1,016 when using long tons and pounds)
- base 10 for integers and base 4 for fractions (lengths in miles and quarter/half miles)
And that’s ignoring specific units for weighing gold, diamonds, etc.
Leonardo of Pisa's famous book "Liber Abaci" spends a lot of time showing how to do arithmetic on these complicated mixed units, and has an interesting notation for them. If you're interested see https://blog.plover.com/math/liber-abaci-fractions.html .
If you enjoy ৪ being four and ৭ seven you will probably enjoy the thousand-year-old magic square inscribed at the Parshvanatha temple in Madhya Pradesh.
https://blog.plover.com/math/magic-square-puzzle.html
Shreevatsa R. tells me that the digit symbols are probably Nagari, which predates Devanagari.
https://play.google.com/store/apps/details?id=com.telugu_num...
Also 6/7 = [2,7,7,14]
so obviously they can factor numbers and they know eighteen is 2*9 and twenty is 2*10 and that they can simplify when dividing 18 by 20, it's just that they don't consider 9/10 a finished result.
For example, if I divide three gold bars between seven people naively, some of them get bars that are 3/7 long and some get three small pieces of 1/7 the amount. If instead I give everyone a 1/4 bar, a 1/7 bar and a 1/28 bar, this is trivially obvious to be fair.
The two people getting the 1/7 + 2/7 pairs can easily verify they are not getting shortchanged, simply by putting their next to one of the 3/7 bars to make sure they add up to the right length.
(Someone dividing 7 sacks of grain among 3 people can do something similar. Maybe they compare two shares of grain on a balance.)
But if you're trying to give everyone a 1/4 bar, a 1/7 bar and a 1/28 bar, sure, it's “trivially obvious to be fair” if you believe you can divide a 1/4 bar into seven exactly equal pieces. But you can't, some will be a little bigger and some will be a little smaller. Seriously, have you ever tried to cut something us unmanageable as a metal bar into seven equal pieces?
“The volume of a truncated pyramid in ancient Egyptian papyri”
“Sources of information on Ancient Egyptian mathematics”
“Problems 1-6 of the Rhind mathematical papyrus” (Includes a description of the math for dividing bread rations)