Four Hieroglyphic and Cuneiform Number Tools

1. Egyptian Hieroglyphic Integers

Each order of magnitude from 1 to 10,000,000 has its own character.
There is some ambiguity and confusion in the mathematical literature about whether egyptian numbers should be written from high order to low order (as we do today) or from low order to high order (i.e units first). In fact, they are written from high order to low order. The confusion appears to come from the fact that hieroglyphics were most often written from right to left - and when these are viewed from left to right, they appear backwards. The fonts built around the Unicode standard are set up for left to right printing, so this tool shows high order digits first, and numbers should be read from left to right.
How can you tell the direction of writing? Look for hieroglyphs of birds, animals and people. They face the beginning of the text. For example, the hieroglyph for 100,000 is 𓆐, which faces LEFT. Thus you would read 𓆐𓆽 as from LEFT to RIGHT as 100,000 + 2,000 (102,000).

Note that cuneiform did not have a character for "0" until about 300 BCE-and even then, it was only used medially. (My tool does not provide any support for a medial zero.) Thus, there is some ambiguity in the meaning of number representation. Similarly, there is no way of differentiating between the integer and fractional portions of a number. For example, the following numbers will all display as
- 𒐗 𒐗: 38880003, 10803
- 𒌍 𒌍: 108030,1830, 30.5
(Try them!)
This function outputs the Babylonian number in two formats: (base 60 integers ; base 60 fractions) and also in Cuneiform.
Sexagesimal orders of magnitude: ... 216,000 3,600 60 1 ; \( \frac{1}{60} \frac{1}{3,600} \frac{1}{216,000} ...\)
The problem of "infinite fractions" is significant and it renders results almost unreadable, so I have rounded fractional parts. You need to be aware of this when looking at the output. I'm not really happy with this solution, so I may revisit it if I get a chance. If I do, I will update this text.
NOTE: You may find that the web font (on Windows) is missing the glyph for the number "20" (U+12399). But you can display the "𒎙" character in another application if you copy a string containing the "missing glyph" glyph to the clipboard and then paste it into an application that uses a font that does have that glyph.

The standard method for writing a Babylonian number in Latin characters is (s,s,s;s,s) where:

the entire expression is surrounded by parentheses ().
s is a sexagesimal digit from 0-59, and
";" is used as a "decimal" point.
Example: 192.5₁₀ (3*60¹ + 12*60⁰ + 30*60^-1 = 192.5) would be entered as (3,12;30)

Sexagesimal orders of magnitude: ... 216,000 3,600 60 1 ; \( \frac{1}{60} \frac{1}{3,600} \frac{1}{216,000} ... \)

This function takes a single binary arithmetic expression containing sexagesimal numbers and outputs its result in sexagesimal and decimal.
Input format is: (sexagesimal number) operation (sexagesimal number)
For example: (3,12;5,2) * (2,2)
Operations supported are:
- + addition
- - subtraction
- * multiplication
- / division
Make sure you include the parentheses around the sexagesimal numbers!
The problem of "infinite fractions" is significant and it can render results almost unreadable, so I have rounded fractional parts. You need to be aware of this when looking at the output. I'm not really happy with this solution, so I may revisit it if I get a chance. If I do, I will update this text.
Currently, the calculator works internally by converting the sexagesimal numbers to decimal, performing the calculation, and then converting the answer back to sexagesimal. This can cause problems if the decimal representation of a fraction has many/infinite places. For example (0;20)*(0;20) should produce (0;6,40), but it actually generates (0;6,39,59,45,35). I may look at rewriting the core code to do everything in sexasgesimal.
Note: The calculator is very brittle, as I have not had time to write much input validation or error handling code. I've given you a bit of leeway as far as putting in some blank spaces, but I'm afraid that's about it. 😀 Similarly, it does not support expressions with more than one operator, so you can't enter an expression like (s₁) + (s₂) + (s₃). 😢