Saturday, October 8, 2016

GNC/K: Greek Numeral Converter/Keyboard

Update Oct 11, 2016

Greek Numeral Converter

INPUT

GNC

15 digits (hundred trillion) maximum and positive integer.
GNC converts modern Arabic (international) numeral ► Greek numeral.


Greek Numeral Keyboard

INPUT KEYBOARD

GNK

15 digits (hundred trillion) maximum.
GNK converts Greek Numeral ► Arabic (international) numeral.

The keyboard input system isn't like the decimal system we use everyday, this has different sequence. Therefore, in order to filter incorrect input, it will just add the number value from the clicked button.
Try it out then.


Greek Numeral List


Method

It's kinda not like today's numeral system (modern Arabic -- straight forward 0-9 decimal), and it's using Greek letter (numeral). And to make it different than just letter (to form a word or not, but not number), it has that symbol that looks like an apostrophe but it's not, behind the number sequence.
And there's the M, as in Myriad, for the power of 10,000. It's not like M in Roman, which is 1,000.

So we use the power of 10, right, like 1,234 = [1 × 103] + [2 × 102] + [3 × 101] + [4 × 100] = 1,000 + 200 + 30 + 4.

The Greek numeral system in that time was not exactly like in our period. They had a letter representation for each number until 9,000. You can see on the table above. So, after 9,999 is Myriad (M) or alpha Myriad (αM). And so forth.

For your information, M = 10,000

The format for Myriad is usually using that superscript writing format with the numbers (multipliers) are above the M letter. This one just rises the numbers position a bit and put color on them so that you know it's the Myriad part.

Let's see some examples:

  • 1 ► αʹ
  • 12 ► 10 + 2 ► ιβʹ
  • 123 = 100 + 20 + 3 ► ρκγʹ
  • 1,234 = 1,000 + 200 + 30 + 4 ► ͵ασλδʹ
  • 12,345 = [10,0001 × 1] + 2,000 + 300 + 40 + 5 ► αMα͵βτμεʹ
  • 123,456 = [10,0001 × (10 + 2)] + 3,000 + 400 + 50 + 6 ► αMιβ͵γυνϛʹ
  • 1,234,567 = [10,0001 × (100 + 20 + 3)] + 4,000 + 500 + 60 + 7 ► αMρκγ͵δφξζʹ
  • And all...

As you can see from the 3 last examples, each has Myriad in it. The alpha before the Myriad is the exponent or power, in this case 1 (α). So it has 10,0001. If the value is one hundred million, for instance 100,000,000 ► βMαʹ (beta myriad alpha) ► 10,0002 × 1 = 100,000,000.


Because this isn't using pen and paper, let's try to read the un-formatted number...

Keep in mind, if there's M, then the letter before M will be used as the exponent.

If there's one M and no letter written before it (on left side), meaning 10,000 powered by α (1).
Like 1x or 1a is written as x or a, sort of.
And for formatted (using pen and paper) writing, the exponent before M can be omitted.

M = 10,000

A large number:

βM͵ααM͵α͵αιαʹ
There's β (2) in front of first M and α (1) in front of second M.
Group it: (βM͵α) (αM͵α) (͵αια)ʹ
Break it down:
► [Mβ × ͵α] + [Mα × ͵α] + ͵α + ι + α
Substitute each letter with its value from the table:
M = 10,000
β = 2
͵α = 1,000
α = 1
ι = 10
► [10,0002 × 1,000] + [10,0001 × 1,000] + 1,000 + 10 + 1
► 100,000,000,000 + 10,000,000 + 1,000 + 10 + 1
100,010,001,011
(one hundred billion, ten mullion, one thousand and eleven)
Also can be written as M͵αM͵α͵αιαʹ (without the exponent in front of M, semi-formatted).

Let's read a smaller number:

αMιε͵βραʹ
There's α (1) in front of first M.
Group it: (αMιε) (͵βρα)ʹ
Break it down:
► [Mα × (ι + ε)] + ͵β + ρ + α
Substitute each letter with its value from the table:
M = 10,000
ι = 10
ε = 5
α = 1
͵β = 2,000
ρ = 100
► [10,0001 × (10 + 5)] + 2,000 + 100 + 1
► 150,000 + 2,000 + 100 + 1
152,101
(one hundred fifty two thousand and one hundred one)
Also can be written as Mιε͵βραʹ (without the exponent in front of M, semi-formatted).

Pay attention on how the grouping technique works for letter surrounding the M (10,000) above. The multiplier sequence for Myriad: thousandth ► hundredth ► tenth ► ones.

Like so: exponent M [thousandth, hundredth, tenth, ones]


Other smaller number without Myriad:

͵αφοʹ
We don't need to group it, it doesn't have myriad part.
Break it down:
► ͵α + φ + ο
Substitute each letter with its value from the table:
͵α = 1,000
φ = 500
ο = 70
► 1,000 + 500 + 70
1,570
(one thousand five hundred and seventy)


As you probably notice, the power (exponent) notation is the opposite version of what we use today. We directly use 103 for 1,000 for example, but not in Greek numeral. It has that right to left writing system feeling, but not really.

Right then, you might want to try it out on the tool above to see other sequences.

GNC has been fixed. The digit is now clustered in the process.