From: Willi Egger via ntg-context <ntg-context@ntg.nl>
To: mailing list for ConTeXt users <ntg-context@ntg.nl>
Cc: Willi Egger <w.egger@boede.nl>
Subject: Re: [NTG-context] Kaktovik numerals
Date: Wed, 19 Apr 2023 20:36:26 +0200 [thread overview]
Message-ID: <FC300CDA-74EB-4FA1-A016-09EC074D4372@boede.nl> (raw)
In-Reply-To: <9cea297c-2d20-f3fc-2fd6-5a46a974873f@fiee.net>
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Hi all,
after playing around and watching YouTube the attached composition is made…
Willi
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[-- Attachment #3: kaktovik-numerals-info.tex --]
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% ConTeXT file
% filename: kaktovik-numerals-intro.tex
% W. Egger
% 19-04-2023
\input meta-imp-kaktovik.mkxl
\definefontfeature
[default]
[default]
[metapost=kaktovik]
\setupbodyfont[dejavu]
\setuppagenumbering[location=footer]
\setuplayout
[header=0pt]
\starttext
\starttitle[title=Kaktovik-numerals]
\startsubject[title=Intro]
On 18-04-2023 Haraban Ramm posted on the mailing-list about the Kaktovik numerals.
\blank
https://mathstodon.xyz/@johncarlosbaez/110215432175491555
\blank
The Inuit have a counting system based on the base 20. Back in 1994 in the local school at Kaktovik in Alaska students developed a counting system for the local language on the base 20. There is a subunit in the form of 5.
The counting system with base 20 is known in different cultures. e.g. The Mayans (Mexico) used a system with dots and horizontal bars.
Even in modern languages there are traces of the base 20 counting system. e.g. French express 80 as \quote{quatre-vingt} and 90 as \quote{quatre-vingt-dix}...
\stopsubject
\startsubject[title=Hans Hagen's implementation]
A couple of hours after Hraban's post, Hans came already up with an implementation of the Kaktovik-numeral-shapes in \METAFUN.
\blank
meta-imp-kaktovik.mkxl
\stopsubject
\startsubject[title=Further information on the Kaktovik-numerals-system]
https://www.youtube.com/watch?v=EyS6FfczH0Q&ab_channel=Artifexian
https://www.youtube.com/watch?v=fIZB4bRwxqI&ab_channel=Dave%27sMathVideos
https://www.youtube.com/watch?v=ObRFHiU_r9I&ab_channel=TheFerret
\stopsubject
\startsubject[title=The key to writing numbers in Kaktovik system]
In order to understand how numbers are composed hereunder is the way in the decimal and in the Kaktovik system.
\bTABLE
\bTR
\bTD[nx=4,align=center] Decimal \eTD
\bTD \strut \eTD
\bTD[nx=4,align=center] Kaktovik \eTD
\eTR
\bTR
\bTD $10^3$ \eTD
\bTD $10^2$ \eTD
\bTD $10^1$ \eTD
\bTD $10^0$ \eTD
\bTD \strut \eTD
\bTD $20^3$ \eTD
\bTD $20^2$ \eTD
\bTD $20^1$ \eTD
\bTD $20^0$ \eTD
\eTR
\bTR
\bTD 1 \eTD
\bTD 0 \eTD
\bTD 0 \eTD
\bTD 0 \eTD
\bTD \strut \eTD
\bTD 8 \eTD
\bTD 0 \eTD
\bTD 0 \eTD
\bTD 0 \eTD
\eTR
\eTABLE
The following table shows the relation between the vertical bars (1 to 4) and the horizontal bars tuplets of 5
\blank
\bTABLE
\setupTABLE[r][each][frame=off,align=flushright]
\setupTABLE[r][even][style=\tfxx]
\setupTABLE[r][odd][style=\tfd]
\setupTABLE[c][1][frame=on]
\setupTABLE[r][1][frame=on]
\bTR
\bTD[frame=off] \kaktoviknumerals{0}\eTD
\bTD \kaktoviknumerals{1}\eTD
\bTD \kaktoviknumerals{2}\eTD
\bTD \kaktoviknumerals{3}\eTD
\bTD \kaktoviknumerals{4}\eTD
\eTR
\bTR
\bTD 0\eTD
\bTD 1\eTD
\bTD 2\eTD
\bTD 3\eTD
\bTD 4\eTD
\eTR
\bTR
\bTD \kaktoviknumerals{5}\eTD
\bTD \kaktoviknumerals{6}\eTD
\bTD \kaktoviknumerals{7}\eTD
\bTD \kaktoviknumerals{8}\eTD
\bTD \kaktoviknumerals{9}\eTD
\eTR
\bTR
\bTD 5\eTD
\bTD 6\eTD
\bTD 7\eTD
\bTD 8\eTD
\bTD 9\eTD
\eTR
\bTR
\bTD \kaktoviknumerals{10}\eTD
\bTD \kaktoviknumerals{11}\eTD
\bTD \kaktoviknumerals{12}\eTD
\bTD \kaktoviknumerals{13}\eTD
\bTD \kaktoviknumerals{14}\eTD
\eTR
\bTR
\bTD 10\eTD
\bTD 11\eTD
\bTD 12\eTD
\bTD 13\eTD
\bTD 14\eTD
\eTR
\bTR
\bTD \kaktoviknumerals{15}\eTD
\bTD \kaktoviknumerals{16}\eTD
\bTD \kaktoviknumerals{17}\eTD
\bTD \kaktoviknumerals{18}\eTD
\bTD \kaktoviknumerals{19}\eTD
\eTR
\bTR
\bTD 15\eTD
\bTD 16\eTD
\bTD 17\eTD
\bTD 18\eTD
\bTD 19\eTD
\eTR
\eTABLE
\stopsubject
\startsubject[title=Examples]
\starttabulate[|r|Mr|r|]
\NC 20 \NC 1 \times 20^1 + 0 \times 20^0\NC \kaktoviknumerals{1}\kaktoviknumerals{0} \NC\NR
\NC 30 \NC 1 \times 20^1 + 10 \times 20^0\NC \kaktoviknumerals{1}\kaktoviknumerals{10} \NC\NR
\NC 40 \NC 2 \times 20^1 + 0 \times 20^0 \NC \kaktoviknumerals{2}\kaktoviknumerals{0} \NC\NR
\NC 100 \NC 5 \times 20^1 + 0 \times 20^0\NC \kaktoviknumerals{5}\kaktoviknumerals{0} \NC\NR
\NC 1000 \NC 2 \times 20^2 + 10 \times 20^1 + 0 \times 20^0
\NC \kaktoviknumerals{2}\kaktoviknumerals{10}\kaktoviknumerals{0}\NC\NR
\NC 2023 \NC 5 \times 20^2 + 0 \times 20^1 + 3 \times 20^0
\NC \kaktoviknumerals{5}
\kaktoviknumerals{0}\kaktoviknumerals{1}\kaktoviknumerals{3}\NC\NR
\stoptabulate
\blank
So the date of today would be:
\blank
19 - 4 - 2023
\blank
\kaktoviknumerals{19} -- \kaktoviknumerals{4} --
\kaktoviknumerals{5}\kaktoviknumerals{0}\kaktoviknumerals{1}\kaktoviknumerals{3}
\blank
Frappant is the possibility to solve arithmetic visually with these Kaktovik-numerals. The approach is to look how patterns fit in the left and right part of the equation.
\starttabulate[|Ml|l|][EQ={$\rightarrow$}]
\NC \rm Decimal \NC Kaktovik \NC\NR
\NC 2 + 2 = 4
\EQ
\kaktoviknumerals{2} $+$ \kaktoviknumerals{2} $=$ \kaktoviknumerals{4}
\NC\NR
\NC 17 - 7 = 10
\EQ
\kaktoviknumerals{17} $-$ \kaktoviknumerals{7} $=$ \kaktoviknumerals{10}
\NC\NR
\NC 1503 / 3
\EQ
\kaktoviknumerals{3}\kaktoviknumerals{15}\kaktoviknumerals{3} $/$ \kaktoviknumerals{3} $=$ \kaktoviknumerals{1}\kaktoviknumerals{5}\kaktoviknumerals{1}
\NC\NR
\NC 364 / 3
\EQ
\kaktoviknumerals{18}\kaktoviknumerals{4} $/$ \kaktoviknumerals{3} $=$ \kaktoviknumerals{6}\kaktoviknumerals{1} remainder \kaktoviknumerals{1}
\stoptabulate
\stopsubject
\stoptitle
\stoptext
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> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context <ntg-context@ntg.nl> wrote:
>
> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
>
> This makes simple calculations just beautiful.
>
> Hraban
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
>
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
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If your question is of interest to others as well, please add an entry to the Wiki!
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archive : https://bitbucket.org/phg/context-mirror/commits/
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___________________________________________________________________________________
next prev parent reply other threads:[~2023-04-19 18:36 UTC|newest]
Thread overview: 14+ messages / expand[flat|nested] mbox.gz Atom feed top
2023-04-18 8:57 Henning Hraban Ramm via ntg-context
2023-04-18 9:23 ` Arthur Rosendahl via ntg-context
2023-04-18 13:01 ` Hans Hagen via ntg-context
2023-04-18 13:52 ` Willi Egger via ntg-context
2023-04-19 12:29 ` Henning Hraban Ramm via ntg-context
2023-04-18 13:41 ` Willi Egger via ntg-context
2023-04-18 15:50 ` Rudolf Bahr via ntg-context
2023-04-18 17:19 ` Otared Kavian via ntg-context
2023-04-19 15:17 ` Willi Egger via ntg-context
2023-04-19 18:36 ` Willi Egger via ntg-context [this message]
2023-04-19 18:58 ` Gavin via ntg-context
2023-04-19 20:45 ` Willi Egger via ntg-context
2023-04-19 21:41 ` Hans Hagen via ntg-context
2023-04-20 16:06 ` Willi Egger via ntg-context
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