From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: X-Spam-Status: No, score=-0.9 required=5.0 tests=MAILING_LIST_MULTI, RCVD_IN_DNSWL_NONE,URIBL_SBL_A autolearn=ham autolearn_force=no version=3.4.4 Received: (qmail 2191 invoked from network); 19 Apr 2023 20:45:41 -0000 Received: from zapf.ntg.nl (5.39.185.232) by inbox.vuxu.org with ESMTPUTF8; 19 Apr 2023 20:45:41 -0000 Received: from localhost (localhost [127.0.0.1]) by zapf.ntg.nl (Postfix) with ESMTP id 94266345; Wed, 19 Apr 2023 22:45:26 +0200 (CEST) X-Virus-Scanned: Debian amavisd-new at zapf.ntg.nl Received: from zapf.ntg.nl ([127.0.0.1]) by localhost (zapf.ntg.nl [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id fcc8wmI9Fk8P; Wed, 19 Apr 2023 22:45:25 +0200 (CEST) Received: from zapf.ntg.nl (localhost [127.0.0.1]) by zapf.ntg.nl (Postfix) with ESMTP id 3BB721FD; Wed, 19 Apr 2023 22:45:25 +0200 (CEST) Received: from localhost (localhost [127.0.0.1]) by zapf.ntg.nl (Postfix) with ESMTP id 47B011FD for ; Wed, 19 Apr 2023 22:45:23 +0200 (CEST) X-Virus-Scanned: Debian amavisd-new at zapf.ntg.nl Received: from zapf.ntg.nl ([127.0.0.1]) by localhost (zapf.ntg.nl [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id typYloUip06A for ; Wed, 19 Apr 2023 22:45:21 +0200 (CEST) Received-SPF: Pass (mailfrom) identity=mailfrom; client-ip=185.233.34.149; helo=dane.soverin.net; envelope-from=w.egger@boede.nl; receiver= Received: from dane.soverin.net (dane.soverin.net [185.233.34.149]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits) key-exchange X25519 server-signature RSA-PSS (2048 bits) server-digest SHA256) (No client certificate requested) by zapf.ntg.nl (Postfix) with ESMTPS id 6D4C01B9 for ; Wed, 19 Apr 2023 22:45:21 +0200 (CEST) Received: from smtp.soverin.net (c04smtp-lb01.int.sover.in [10.10.4.74]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits) key-exchange X25519 server-signature RSA-PSS (4096 bits) server-digest SHA256) (No client certificate requested) by dane.soverin.net (Postfix) with ESMTPS id 4Q1t8d17MFz10Nl for ; Wed, 19 Apr 2023 20:45:21 +0000 (UTC) Received: from smtp.soverin.net (smtp.soverin.net [10.10.4.99]) by soverin.net (Postfix) with ESMTPSA id 4Q1t8c1slFzNP for ; Wed, 19 Apr 2023 20:45:20 +0000 (UTC) X-Soverin-Authenticated: true Content-Type: multipart/mixed; boundary="Apple-Mail=_F6045E54-D692-4AF5-9904-609E0F135493" Mime-Version: 1.0 (Mac OS X Mail 14.0 \(3654.120.0.1.15\)) Date: Wed, 19 Apr 2023 22:45:18 +0200 References: <9cea297c-2d20-f3fc-2fd6-5a46a974873f@fiee.net> To: mailing list for ConTeXt users In-Reply-To: Message-Id: <0B0CF438-1FC2-4DAE-9CBD-2F22D1977863@boede.nl> Subject: Re: [NTG-context] Kaktovik numerals X-BeenThere: ntg-context@ntg.nl X-Mailman-Version: 2.1.38 Precedence: list List-Id: mailing list for ConTeXt users List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , From: Willi Egger via ntg-context Reply-To: mailing list for ConTeXt users Cc: Willi Egger Errors-To: ntg-context-bounces@ntg.nl Sender: "ntg-context" --Apple-Mail=_F6045E54-D692-4AF5-9904-609E0F135493 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=utf-8 Hello Gavin, thank you so much for your input. =E2=80=94 Indeed you are right. Please = find attached the corrected version. --Apple-Mail=_F6045E54-D692-4AF5-9904-609E0F135493 Content-Disposition: inline; filename=kaktovik-numerals-info.pdf Content-Type: application/pdf; x-unix-mode=0644; name="kaktovik-numerals-info.pdf" Content-Transfer-Encoding: base64 JVBERi0xLjcKJcPPztTF2NTQxMYKNCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVu Z3RoIDE0OTkgPj4Kc3RyZWFtCnjazVnNbiM3DL7nKfwCOxVF/QJBgNjjKdBzbkWv7anvfy0lUpRk j+PJdhdYYIVYEkVRH/9nzemfkzn9/nL+ePltgxOY08ffL7BA9h4i7ZiTTmzMSwgGgz+FuFhENHj6 +Pf056sxBt7+On388WIXE3xyuZ7USTRLCvEUXV4w00LQY5YG0nA0PI1AI9JIZe0NUqHJNN5pnGlc aKw0rnJuo5sNXw2LQxdUaJm0qw0sxiVvU7saQNh6YRcam723C5sQYYlgLXplU17w/vbNBaww0D9k mYHeBF5+B5mXv7FRQ5JXyGsgy1z5Af2ylTHK4y+6dWa4yjPqGwgW0N0KZBeL9qHAturKRXgmBrH+ JTTgKoDLGnPXU03IIOrwOzccQNG7BTF6d9AMviEbwqdGQGM7crf1S9Gai6rBVS71DCqIPBZ4KFTy RAW8gH9pUJfriZ4OWqK1Ts4TnQ1CuzKdjYPWt65E1f7azxsZzXbKb5vYriAOa7mv2/dOx+MALD57 8m2XvXq0PXebQXSjx5xFM153VhE9jvQG26/65GYzzefU4pSLYfBGiy72LrsCT90VW5d7xNZl5u/k 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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 1000 \eTD \bTD 100 \eTD \bTD 10 \eTD \bTD 1 \eTD \bTD \strut \eTD \bTD 8000 \eTD \bTD 400 \eTD \bTD 20 \eTD \bTD 1 \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 + 1 \times 20^1 + 3 \times 20^0 \NC \kaktoviknumerals{5} \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{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. \blank The presented examples are from: https://www.youtube.com/watch?v=ObRFHiU_r9I&ab_channel=TheFerret \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 --Apple-Mail=_F6045E54-D692-4AF5-9904-609E0F135493 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=utf-8 Willi > On 19 Apr 2023, at 20:58, Gavin via ntg-context = wrote: >=20 > Hi Willi, >=20 > What fun! I think I found a couple math items to correct. >=20 > 1) The second line of the tables at the top of page 2 should be: > 1000' 100, 10, 1; 8000, 400, 20, 1 >=20 > 2) For the year conversion: 2023 =3D 5x20^2 + 1x20 + 3. (Your 0 should = be my 1). This will give a three digit Kaktovik numeral. You have 4 = digit Kaktovik numerals for 2023, with both a 0 and a 1. >=20 > Gavin >=20 >=20 >> On Apr 19, 2023, at 12:36 PM, Willi Egger via ntg-context = wrote: >>=20 >> Hi all, >>=20 >> after playing around and watching YouTube the attached composition = is made=E2=80=A6 >>=20 >> Willi >> >>=20 >>> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context = wrote: >>>=20 >>> 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 >>>=20 >>> This makes simple calculations just beautiful. >>>=20 >>> Hraban >>> = __________________________________________________________________________= _________ >>> If your question is of interest to others as well, please add an = entry to the Wiki! >>>=20 >>> maillist : ntg-context@ntg.nl / = https://www.ntg.nl/mailman/listinfo/ntg-context >>> webpage : https://www.pragma-ade.nl / http://context.aanhet.net >>> archive : https://bitbucket.org/phg/context-mirror/commits/ >>> wiki : https://contextgarden.net >>> = __________________________________________________________________________= _________ >>=20 >> = __________________________________________________________________________= _________ >> If your question is of interest to others as well, please add an = entry to the Wiki! >>=20 >> maillist : ntg-context@ntg.nl / = https://www.ntg.nl/mailman/listinfo/ntg-context >> webpage : https://www.pragma-ade.nl / http://context.aanhet.net >> archive : https://bitbucket.org/phg/context-mirror/commits/ >> wiki : https://contextgarden.net >> = __________________________________________________________________________= _________ >=20 > = __________________________________________________________________________= _________ > If your question is of interest to others as well, please add an entry = to the Wiki! >=20 > maillist : ntg-context@ntg.nl / = https://www.ntg.nl/mailman/listinfo/ntg-context > webpage : https://www.pragma-ade.nl / http://context.aanhet.net > archive : https://bitbucket.org/phg/context-mirror/commits/ > wiki : https://contextgarden.net > = __________________________________________________________________________= _________ --Apple-Mail=_F6045E54-D692-4AF5-9904-609E0F135493 Content-Type: text/plain; charset="us-ascii" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Disposition: inline ___________________________________________________________________________________ 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 webpage : https://www.pragma-ade.nl / http://context.aanhet.net archive : https://bitbucket.org/phg/context-mirror/commits/ wiki : https://contextgarden.net ___________________________________________________________________________________ --Apple-Mail=_F6045E54-D692-4AF5-9904-609E0F135493--