Base Dozen Forumhttps://dozenal.forumotion.com/feed/?Latest topicsfrFri, 05 Aug 2022 12:57:47 GMT10Base Dozen Forumhttps://illiweb.com/fa/m/logo3.gifhttps://dozenal.forumotion.com/feed/?Pasigraphie of Joseph de Maimieuxhttps://dozenal.forumotion.com/t53-pasigraphie-of-joseph-de-maimieuxhttps://dozenal.forumotion.com/t53-pasigraphie-of-joseph-de-maimieuxPhaethon"La Pasigraphie a pour uniques élémens :
1°. Douze caractères qui doivent d'abord être considérés comme n'ayant
ni la forme, ni la destination, ni la valeur convenue d'aucune lettre
d'aucun alphabet. Voici ces douze caractères rangés dans l'ordre qu'on
appellera la GAMME PASIGRAPHIQUE, afin de se ménager la ressource
d'une dénomination réduite aux cinq lettres du mot gamme, qui revien-
dront souvent.
2°. Douze règles générales applicables à toutes les langues, à tous les
dialectes; ...ReferencesFri, 05 Aug 2022 12:57:47 GMThttps://dozenal.forumotion.com/t53-pasigraphie-of-joseph-de-maimieux#165Probabilities of Primes and Compositeshttps://dozenal.forumotion.com/t36-probabilities-of-primes-and-compositeshttps://dozenal.forumotion.com/t36-probabilities-of-primes-and-compositesPhaethonPreamble
The aim here is to discover the frequencies of numbers for the purpose of guiding the selection of a numerical base that best represents the most frequent numbers.
Proposition 1:
Suppose that all natural whole numbers are equally probable.
Caveat:
It is not actually believed that all whole numbers have an equal probability of being selected.
Corollary:
Then, if a number from the set of natural whole numbers be selected at random, each whole number has an equal probability of ...MathematicsSun, 24 Jul 2022 17:22:14 GMThttps://dozenal.forumotion.com/t36-probabilities-of-primes-and-composites#164Base Optimalityhttps://dozenal.forumotion.com/t52-base-optimalityhttps://dozenal.forumotion.com/t52-base-optimalityPhaethonIn the conclusion to the Factor Density topic at https://dozenal.forumotion.com/t51-factor-density, I concluded:
Phaethon, Tue 19th Jun 2022 at 19:44 wrote:This factor density as a computed measure of base efficiency does not penalise an increase in size of the base enough,
In order to furnish a measure of optimality of bases that moves large bases down the league, the factor density \(D_B\) can be multiplied by the measure of another property that decreases with the size of the base. One ...MathematicsSat, 23 Jul 2022 13:28:15 GMThttps://dozenal.forumotion.com/t52-base-optimality#163Factor Densityhttps://dozenal.forumotion.com/t51-factor-densityhttps://dozenal.forumotion.com/t51-factor-densityPhaethonConsider that the most important property of a number for it to be used as a base of enumeration and division is the number of factors it has. Under this supposition, a base with more factors will be better than a base that has fewer factors, while other conditions are equal as far as possible. For example, the base thirty should be a better base than the bases twenty-nine or thirty-one, because thirty has more factors than twenty-nine or thirty-one, although the numbers are of similar size. ...MathematicsThu, 21 Jul 2022 22:46:37 GMThttps://dozenal.forumotion.com/t51-factor-density#162"Lagrange was Wrong, Pascal was Right"https://dozenal.forumotion.com/t49-lagrange-was-wrong-pascal-was-righthttps://dozenal.forumotion.com/t49-lagrange-was-wrong-pascal-was-rightPhaethonBREAKING NEWS June 2022:
https://sciendo.com/it/article/10.2478/rmm-2022-0004
Recreational Mathematics Magazine, Volume 9 (2022), Issue 16 (June 2022), pages 55 - 64.
Article title: "Lagrange was Wrong, Pascal was Right"
The author George Teşeleanu concludes: "Conclusions: According to our experiments the best positional base is the duodecimal system [...] Thus, Pascal was right to propose the use of the duodecimal system instead of the decimalsystem, while Lagrange was wrong ...ReferencesTue, 21 Jun 2022 21:12:19 GMThttps://dozenal.forumotion.com/t49-lagrange-was-wrong-pascal-was-right#159"High-Radix Formats for Enhancing Floating-Point FPGA Implementations"https://dozenal.forumotion.com/t50-high-radix-formats-for-enhancing-floating-point-fpga-implementationshttps://dozenal.forumotion.com/t50-high-radix-formats-for-enhancing-floating-point-fpga-implementationsPhaethonhttps://link.springer.com/content/pdf/10.1007/s00034-021-01855-x.pdf
Circuits, Systems, and Signal Processing (2022) 41:1683–1703
Published online: 2nd December 2021
Article title: "High-Radix Formats for Enhancing Floating-Point FPGA Implementations"
Authors: Julio Villalba, Javier Hormigo
Extracts:
"For applications with similar numbers of additions and multiplications, the
high-radix version may be up to 26% faster"
"We propose using a radix 2^r (with r being an integer and ...ReferencesMon, 20 Jun 2022 18:34:44 GMThttps://dozenal.forumotion.com/t50-high-radix-formats-for-enhancing-floating-point-fpga-implementations#158Twelfths Metric Rulerhttps://dozenal.forumotion.com/t48-twelfths-metric-rulerhttps://dozenal.forumotion.com/t48-twelfths-metric-rulerPhaethonFantastic news! Commercially available, off the shelf trigonal prismatic metric rulers are available in which the centimetre is divided by twelve graduations along one of its six scales. The image shows one such ruler, described as an "Architect Triangular Scale", made of aluminium metal, cool to the touch, aligned with a steel ruler with inches divided in a binary fashion at the top edge and centimetres divided into inches at its other edge. Before acquiring the steel ruler, I was disappointed ...PhaenomenaThu, 16 Jun 2022 18:49:22 GMThttps://dozenal.forumotion.com/t48-twelfths-metric-ruler#156Graduation Subdivisionshttps://dozenal.forumotion.com/t47-graduation-subdivisionshttps://dozenal.forumotion.com/t47-graduation-subdivisionsPhaethonAnyone who has thought about designing a clock face, protractor, ruler, or measuring instrument for a metrological system using a base such as twelve other than decimal is likely to have contemplated what the best way to subdivide the graduation marks would be. As such, this topic has been discussed by others before elsewhere in the context of base twelve and the marks of a straight ruler. I know of the question being asked before but not being answered satisfactorily elsewhere. The following ...MetrologyWed, 15 Jun 2022 14:07:35 GMThttps://dozenal.forumotion.com/t47-graduation-subdivisions#155Optimal Analogue Clockhttps://dozenal.forumotion.com/t46-optimal-analogue-clockhttps://dozenal.forumotion.com/t46-optimal-analogue-clockPhaethonThe Optimal Base, Divisions and Hands for Analogue Clocks
For a clock showing the time in base twelve, some have proposed dividing the day successively by powers of twelve each time, starting for the first division with a division of twelve giving twelve double hours or duors, and that the number of tick marks should be either twelve or the square of twelve. However, these proposals give rise to potential problems in mechanical analogue clocks. So few as only twelve tick marks wastes the angular ...MetrologySun, 12 Jun 2022 00:09:08 GMThttps://dozenal.forumotion.com/t46-optimal-analogue-clock#154Dozenal Numismaticshttps://dozenal.forumotion.com/t45-dozenal-numismaticshttps://dozenal.forumotion.com/t45-dozenal-numismaticsPhaethonFor conversion of the base of arithmetic from decimal to dozenal, it is proposed that the denominations of money should be made at rounded values or factors of the base twelve instead of ten. While it is possible to consider many improvements and innovations in the way money is produced, for the purpose of introduction of base twelve, only those changes that are necessary for implementation of dozenal are recommended as essential, whereas other proposals are advised for later stages provided ...MetrologySat, 14 May 2022 15:53:33 GMThttps://dozenal.forumotion.com/t45-dozenal-numismatics#153Social, Economic, and Political Influences on Dozenismhttps://dozenal.forumotion.com/t44-social-economic-and-political-influences-on-dozenismhttps://dozenal.forumotion.com/t44-social-economic-and-political-influences-on-dozenismPhaethonOne of the benefits of this dozenal forum compared to another one is that this Base Dozen Forum may permit a greater extent of freedom of expression on controversial views relevant to dozenism, whereas another forum may discourage political sentiments as a banning offence.
I myself am interested more in the mathematical discussion around dozenism, have not engaged in overt political expression on Dozens Online, and I can understand how to some of like mind, political expression may be off-putting. ...PhaenomenaMon, 14 Feb 2022 19:45:52 GMThttps://dozenal.forumotion.com/t44-social-economic-and-political-influences-on-dozenism#152QR Codehttps://dozenal.forumotion.com/t43-qr-codehttps://dozenal.forumotion.com/t43-qr-codePhaethonPrint and scan the following QR code to reach the Base Dozen Forum:
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<br />
<img src="https://i.postimg.cc/7Y55rS63/qrcode-dozenal-forumotion-com.png" alt=""/>Forum ManagementSun, 06 Jun 2021 19:48:03 GMThttps://dozenal.forumotion.com/t43-qr-code#151Dozenal Directionshttps://dozenal.forumotion.com/t39-dozenal-directionshttps://dozenal.forumotion.com/t39-dozenal-directionsPhaethonBackground: Prior Art
Cardinal Directions
Older directional names appear for the four cardinal directions originating from a North and South wind axis and a dawn to dusk axis.
The Twelve Classical Wind Directions
Elaboration and refinement of the cardinal directions with intercardinal directions produced eight directions, then extended to twelve by philosophers. Classically in Greek and later in Latin, the twelve directions were named by winds blowing from those directions. These were:
...PhaenomenaMon, 03 May 2021 13:37:44 GMThttps://dozenal.forumotion.com/t39-dozenal-directions#150Pendulum Systemhttps://dozenal.forumotion.com/t23-pendulum-systemhttps://dozenal.forumotion.com/t23-pendulum-systemPhaethonThat Dozenal Transcends Metrology
There are and have been many collections of unrelated units of measurement and more structured systems of units of measurement that have been used at the same time and with one and the same base of numeration for representing the numbers without regard to the way units have been multiplied or aggregated into larger units or subdivided into smaller units of measurement. For example, there have been units of weight that increased as binary powers although their ...MetrologyFri, 12 Feb 2021 18:59:22 GMThttps://dozenal.forumotion.com/t23-pendulum-system#149Troyhttps://dozenal.forumotion.com/t42-troyhttps://dozenal.forumotion.com/t42-troyPhaethonThe troy ounce is legally used for the sale of metal bullion. It is the normal weight by which precious metal prices are quoted. This cannot be changed readily, because of the large number of historical bullion artefacts such as ingots and coins bearing designs used for investment. If they were melted down, it would destroy their provenance.
Twelve troy ounces make a troy pound. A cube of water weighing a troy pound would have an edge length so nearly equal to six dozen or half a dozen dozen ...MetrologyThu, 08 Oct 2020 11:49:34 GMThttps://dozenal.forumotion.com/t42-troy#148Old Irish Metricshttps://dozenal.forumotion.com/t41-old-irish-metricshttps://dozenal.forumotion.com/t41-old-irish-metricsPhaethonOld Irish Units of Measurement Based on Twelve
It has been claimed that evidence from amongst the earliest written texts of Brehon Law from Old Ireland indicates that Irish legal systems of measurement that existed were based fairly consistently on factors of twelve between units. This was before the English system took over in Ireland. Note that plurals in the Irish language were formed differently from how they are translated here for the sake of understanding.
Length
It was proposed that ...MetrologyTue, 29 Sep 2020 16:32:47 GMThttps://dozenal.forumotion.com/t41-old-irish-metrics#147Zenthttps://dozenal.forumotion.com/t40-zenthttps://dozenal.forumotion.com/t40-zentPhaethonA search for the neologism "zent" was done on the DozensOnline forum today. Only four results appeared, suggesting that this word did not have much uptake. The earliest three are dated from the last two months of the decimal year 2013 and by the same author, who proposed it for the second power of twelve.
This word could be proposed for a square twelfth that would sound similar to the word "cent" used for specifying musical pitches with minimum change. A cent is a hundredth root of the frequency ...NomenclatureMon, 28 Sep 2020 13:12:25 GMThttps://dozenal.forumotion.com/t40-zent#146Air Current Zoneshttps://dozenal.forumotion.com/t38-air-current-zoneshttps://dozenal.forumotion.com/t38-air-current-zonesPhaethon
Image from: "Figure 7.5 in The Atmosphere, 8th edition, Lutgens and Tarbuck, 8th edition, 2001."
In the atmosphere of planet Earth, circulating currents of air are divided into latitudinal zones called cells.
The Sun heats the atmosphere at the equator, causing warm air to rise from the surface of the Earth, resulting in a low pressure system equatorially. A current of surface air moves towards the equator from other latitudes to fill the low pressure. Due to the rotation of the Earth ...PhaenomenaTue, 01 Sep 2020 14:08:14 GMThttps://dozenal.forumotion.com/t38-air-current-zones#144Font CSShttps://dozenal.forumotion.com/t32-font-csshttps://dozenal.forumotion.com/t32-font-cssPhaethonPreceding text<link href="https://fonts.googleapis.com/css?family=Italianno&display=swap" rel="stylesheet"><div style="font-family: 'Italianno', cursive;"><span style="font-size: 24px; line-height: normal">Italianno</span></div>Superseding textForum ManagementSun, 03 May 2020 08:14:48 GMThttps://dozenal.forumotion.com/t32-font-css#143Vector Imageshttps://dozenal.forumotion.com/t37-vector-imageshttps://dozenal.forumotion.com/t37-vector-imagesPhaethon Code: <iframe src='https://svgshare.com/i/F3Y.svg' width=25% height=25% ></iframe>
Code: <img src="https://svgshare.com/i/F3Y.svg" style="max-width:6.25%;">
Forum ManagementSat, 18 Apr 2020 07:03:44 GMThttps://dozenal.forumotion.com/t37-vector-images#139MathJaxhttps://dozenal.forumotion.com/t4-mathjaxhttps://dozenal.forumotion.com/t4-mathjaxPhaethonLatex example:
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\sum_{n = 4}^{n = 0}n^2Forum ManagementSun, 12 Apr 2020 20:58:55 GMThttps://dozenal.forumotion.com/t4-mathjax#135Character for Elevenhttps://dozenal.forumotion.com/t35-character-for-elevenhttps://dozenal.forumotion.com/t35-character-for-elevenPhaethonBoth the American and British dozenal societies used a symbol of Pitman like a turned digit three for representing the number eleven. A problem with this symbol is that it looks too much like a lower case Greek letter epsilon ε or open letter Ɛ often used in mathematics and in physics. There were variations on its design, such as by Dwiggins, to make it look different from the letter.
A proposal for a character representing the number eleven is like a Gothic arch. It is derived from the joining ...NumeralsFri, 10 Apr 2020 15:31:05 GMThttps://dozenal.forumotion.com/t35-character-for-eleven#134Conditions for Numerical Character Designhttps://dozenal.forumotion.com/t34-conditions-for-numerical-character-designhttps://dozenal.forumotion.com/t34-conditions-for-numerical-character-designPhaethonIf a symbol is to be designed for representing a numeral, there are some characteristics it should have.
1. It should be distinct from characters used for other purposes so that it will not be confused with those other characters. The character designed for representing a number should not look the same as a letter, especially in mathematics such as algebra where letters are used to represent variables. A symbol that is already commonly used in mathematical notation should not be borrowed ...NumeralsFri, 10 Apr 2020 09:16:11 GMThttps://dozenal.forumotion.com/t34-conditions-for-numerical-character-design#133The Metgloss (Wendy Krieger)https://dozenal.forumotion.com/t33-the-metgloss-wendy-kriegerhttps://dozenal.forumotion.com/t33-the-metgloss-wendy-kriegerwendy.kriegerThis is a series of webpages, which are more about ideas behind a measurement system, rather than individual units etc.
It is essentially the working notes on metrology since 1983, along with tables of values. Multiple bases are discussed.
http://www.os2fan2.com/mgloss/index.html The metgloss
http://www.os2fan2.com/mglossn/index.html as nature intended (same file, but with þ for th). ReferencesMon, 27 Jan 2020 12:27:12 GMThttps://dozenal.forumotion.com/t33-the-metgloss-wendy-krieger#132Myon Dozenal Nomenclaturehttps://dozenal.forumotion.com/t25-myon-dozenal-nomenclaturehttps://dozenal.forumotion.com/t25-myon-dozenal-nomenclaturePhaethonThis system of names for powers of twelve is inspired from the Duodecimal Myriad System nomenclature proposed by Takashi, 1st March 2019, http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/revised.pdf and the derivative Dozenal Mylliad Nomenclature, https://dozenal.forumotion.com/t8-dozenal-mylliad-nomenclature.
Positive exponents indicated by dozenal "digits" to the left of the fractional point or dozenal zot produce a suffix -on.
Negative exponents indicated by numerical figure characters to ...NomenclatureTue, 14 Jan 2020 18:34:34 GMThttps://dozenal.forumotion.com/t25-myon-dozenal-nomenclature#131Dozenal Mylliad Nomenclaturehttps://dozenal.forumotion.com/t8-dozenal-mylliad-nomenclaturehttps://dozenal.forumotion.com/t8-dozenal-mylliad-nomenclaturePhaethonThis is an adaptation of the Duodecimal Myriad System nomenclature system proposed by Takeshi, 1st March 2019, http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/revised.pdf.
It copies the multiplicative principle of natural language ordinarily used by the common majority whereby indices or exponents are not stated explicitly while powers are attained as the products of terms for smaller powers of the base. The words dozen and gross already in English for powers of twelve are retained.
Components ...NomenclatureSat, 23 Nov 2019 07:22:05 GMThttps://dozenal.forumotion.com/t8-dozenal-mylliad-nomenclature#127Mnemonicshttps://dozenal.forumotion.com/t27-mnemonicshttps://dozenal.forumotion.com/t27-mnemonicsPhaethonThere has been an appeal for a system of mnemonics by which dozenal figures could be remembered using words (SenaryThe12th, Dozens Online, https://www.tapatalk.com/groups/dozensonline/request-for-help-with-mnemonics-for-dozenal-t2020.html).
SenaryThe12th, 4:54 PM - Sep 30, #47, https://www.tapatalk.com/groups/dozensonline/so-how-difficult-are-the-multiplication-tables-of--t2045-s24.html wrote:Oh man, the holy grail for me would be a system of mnemonics which worked as well for dozenal as for ...NomenclatureFri, 22 Nov 2019 11:24:12 GMThttps://dozenal.forumotion.com/t27-mnemonics#126Tableshttps://dozenal.forumotion.com/t31-tableshttps://dozenal.forumotion.com/t31-tablesPhaethonHTML Table test:
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<table border=1 > <tr><td>cell 1</td><td>cell 2</td><td>cell 3</td></tr> <tr><td>cell 4</td><td>cell 5</td><td>cell 6</td></tr> </table>
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End HTML table test.
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BBCode Table comparison:
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<table cellspacing="0" class="posting-table"><tr><td>Cell 1</td><td>Cell 2</td></tr><tr><td>Cell 3</td><td>Cell 4</td></tr></table>Forum ManagementFri, 22 Nov 2019 10:08:13 GMThttps://dozenal.forumotion.com/t31-tables#124Pyritohedral crystalhttps://dozenal.forumotion.com/t30-pyritohedral-crystalhttps://dozenal.forumotion.com/t30-pyritohedral-crystalPhaethon
The three images above show photographs of the mineral pyrite as a crystal having twelve faces. This specimen is not perfectly regular.
How to determine when such crystals are genuine habits rather than sliced or faceted is an interesting question. I must attempt to measure or calculate the dihedral angles, though this may require a special instrument to do accurately, as the spokes of most protractors are not continued to such a small scale size. In this sample, pairs of opposite faces ...PhaenomenaSun, 27 Oct 2019 22:46:05 GMThttps://dozenal.forumotion.com/t30-pyritohedral-crystal#123Ratios of Decimal and Dozenal Powershttps://dozenal.forumotion.com/t29-ratios-of-decimal-and-dozenal-powershttps://dozenal.forumotion.com/t29-ratios-of-decimal-and-dozenal-powersPhaethonWhereas when a single base of numeration may be used, its basic arithmetic could be done mentally quickly provided certain tables such as for multiplication be learnt, while two bases co-exist such as when one is being for a period of time supplanted by the other, there would be a benefit to more rapid mental calculation in learning additional facts, over those of a single base, for the purpose of conversion between the two bases until one of them becomes the exclusive base.
While conversion ...MathematicsSat, 26 Oct 2019 13:12:06 GMThttps://dozenal.forumotion.com/t29-ratios-of-decimal-and-dozenal-powers#120The design of the C.O.F. systemhttps://dozenal.forumotion.com/t22-the-design-of-the-c-o-f-systemhttps://dozenal.forumotion.com/t22-the-design-of-the-c-o-f-systemwendy.kriegerThe basic rules follow those provided here: https://www.tapatalk.com/groups/twelftyonline/on-designing-new-systems-t47.html
Getting density and velocity right in any given system provides more 'true to scale' units. But in place of a time unit, we select gravity as the additional base unit.
The measure \( v/g\) velocity/gravity = time, is chosen to keep gravity as unity, and the velocity as in the human range. This table gives the present common velocities, the velocity and the derived ...MetrologyTue, 15 Oct 2019 08:38:08 GMThttps://dozenal.forumotion.com/t22-the-design-of-the-c-o-f-system#112Hexadactylyhttps://dozenal.forumotion.com/t28-hexadactylyhttps://dozenal.forumotion.com/t28-hexadactylyPhaethonPanda paws
I read today that a mascot of the Dozenal Society of America was the giant panda bear.
M1n1f1g, 05-Jan-2012 00:39:35, #10, https://forum.colemak.com/topic/1325-dozenal-support/ wrote:You know, the Dozenal Society of America's mascot is a panda. They have 6 digits on each hand, apparently.
https://upload.wikimedia.org/wikipedia/commons/0/0f/Giant_panda_Left_hand_Bone_2.jpg by Momotarou2012.
Panda Hand by Travis, on Flickr
The sixth not being a true digit, is an enlarged ...PhaenomenaFri, 11 Oct 2019 20:43:53 GMThttps://dozenal.forumotion.com/t28-hexadactyly#110Dozenalizing Metrichttps://dozenal.forumotion.com/t3-dozenalizing-metrichttps://dozenal.forumotion.com/t3-dozenalizing-metricPhaethonOn the Twelfty Online forum, in a topic on dozenal at https://www.tapatalk.com/groups/twelftyonline/dozenalising-the-metric-system-t24.html, Wendy decided that the appropriate size of unit of length at the human scale of measurement is on the order of the decimetre.
wendy.krieger Oct 03, 2018 wrote:The sorts of numbers one encounters in life-size objects are best expressed in decimetres,
The choice of sizes of base units of measurement may be argued by observation of the units of the decimal ...MetrologyFri, 11 Oct 2019 17:35:53 GMThttps://dozenal.forumotion.com/t3-dozenalizing-metric#109Proto-Indo-European Numbershttps://dozenal.forumotion.com/t26-proto-indo-european-numbershttps://dozenal.forumotion.com/t26-proto-indo-european-numbersPhaethonIndo-European languages are the most widespread and international on Earth. As can be guessed from the name, most languages of Europe are of Indo-European origin, and consequently so too are languages of their global former colonies. The primary languages of most people in the Americas are Indo-European. Included are very major lingua francas or languages of international communication in diplomacy, science, and commerce, such as Spanish, Portuguese, French, German, and English. Classical European ...NomenclatureWed, 02 Oct 2019 19:46:34 GMThttps://dozenal.forumotion.com/t26-proto-indo-european-numbers#101Dozenal Fifths Better than Decimal Thirdshttps://dozenal.forumotion.com/t24-dozenal-fifths-better-than-decimal-thirdshttps://dozenal.forumotion.com/t24-dozenal-fifths-better-than-decimal-thirdsPhaethonSevenths
The prime number seven is not a factor of ten. Consequently, the fraction a seventh written in decimal form does not terminate. The digits after the decimal fractional jot repeat after cycles of six digits for sevenths. The maximum number of digits in the representation of a unit fraction 1/p that is the reciprocal of a prime number p by positional notation of some base B before repetition of the cycle is p - 1, which is one less than the prime number. In decimal a seventh has the maximum ...MathematicsFri, 20 Sep 2019 14:38:05 GMThttps://dozenal.forumotion.com/t24-dozenal-fifths-better-than-decimal-thirds#95No more than Six Regular 4-Dimensional Figureshttps://dozenal.forumotion.com/t21-no-more-than-six-regular-4-dimensional-figureshttps://dozenal.forumotion.com/t21-no-more-than-six-regular-4-dimensional-figuresPhaethonTessellations of the regular figures lead to the symmetries of division of angles that the base of numeration should be chosen to represent compactly. Not all regular figures tessellate the Euclidean non-curved spaces of area and volume and capacities of higher dimensions.
Whereas other mathematicians may mean by a circle its circumference, and by a sphere its surface, here rather a circle would be the circumference and the disk, and a sphere would be the surface and the volume, the radius ...MathematicsMon, 09 Sep 2019 10:51:26 GMThttps://dozenal.forumotion.com/t21-no-more-than-six-regular-4-dimensional-figures#83Dozenal Nomenclature of Geometrical Figureshttps://dozenal.forumotion.com/t20-dozenal-nomenclature-of-geometrical-figureshttps://dozenal.forumotion.com/t20-dozenal-nomenclature-of-geometrical-figuresPhaethonA proposal for replacing decimal based names of geometrical figures by dozenal names of Greek derivation.
Table of Names for Polygons
Number of Vertices or Edges Polygon Name Notes one henagon pointtwo digon segment of a linethree trigon trianglefour tetragon quadrilateralfive pentagonsix hexagonseven heptagoneight octagonnine enneagonnonagonten decagoneleven enkomigontwelve henzigona dozen plus one henkaizigona dozen plus two dokaizigona dozen plus three trikaizigon includes ...NomenclatureMon, 09 Sep 2019 06:52:16 GMThttps://dozenal.forumotion.com/t20-dozenal-nomenclature-of-geometrical-figures#81Comments on Angle Unitshttps://dozenal.forumotion.com/t18-comments-on-angle-unitshttps://dozenal.forumotion.com/t18-comments-on-angle-unitswendy.kriegerThere are three different kinds of circle, which use separate units and constructs.
Circles in the sky, measured in units of time and calendar.
Real circles, measured by their diameters, the value \( \pi\) measures the roll against diameter.
Arcs, which are measured by right variation at a distance.
Circles in the sky are measured according to the day-cycle (equatorial circles give a zenith-marker pointing to siderial noon), and the elliptic traces out the movements of the sun, the ...MetrologySat, 07 Sep 2019 12:14:26 GMThttps://dozenal.forumotion.com/t18-comments-on-angle-units#74Angles in Construction Graphicshttps://dozenal.forumotion.com/t19-angles-in-construction-graphicshttps://dozenal.forumotion.com/t19-angles-in-construction-graphicsPhaethonThere are a number of conventions by which models in three dimensions are presented on a two-dimensional page. The following approaches do not involve perspective stereography.
1. Oblique Drawing
Figure 1. Oblique cube
In an oblique drawing, one of the co-ordinate planes of space is viewed directly facing the eye, while the dimension of the three-dimensional space that is perpendicular to that co-ordinate plane is on the page drawn obliquely halfway between the other two co-ordinate axis ...MetrologySun, 01 Sep 2019 15:59:20 GMThttps://dozenal.forumotion.com/t19-angles-in-construction-graphics#58Angular to Rectangularhttps://dozenal.forumotion.com/t16-angular-to-rectangularhttps://dozenal.forumotion.com/t16-angular-to-rectangularPhaethonThe complete angle for a full turn or perigon of a circle, which is 360 degrees or \(2\pi\) radians, may be divided into sectors in number equal to a base, \(B \). The angle of a sector would be of the perigon a \(B\)th part, that is, 360/\(B\) mesopotamian degrees written decimally or \(2\pi/B\) radians.
A circle may be plotted in a plane of rectangular co-ordinates \(x\) and \(y\), where the co-ordinate axes are perpendicular to each other and of the same scale, letting the centre of the ...MathematicsSat, 31 Aug 2019 14:22:09 GMThttps://dozenal.forumotion.com/t16-angular-to-rectangular#57Star Mapshttps://dozenal.forumotion.com/t17-star-mapshttps://dozenal.forumotion.com/t17-star-mapsPhaethonFormation of a dozenal metrological system with minimum change to current measures would suggest retention of scales being used that are already partitioned dozenally and making such units the foundation of an integrated dozenal system.
Quantities which were not successfully reckoned in decimal include angle, where 360 or two-and-a-half square dozen degrees to a circle persist, and time of hours, minutes, and seconds, partly based on sexagesimal or base sixty which is a multiple of twelve. ...MetrologySat, 31 Aug 2019 10:39:02 GMThttps://dozenal.forumotion.com/t17-star-maps#54Co-existing baseshttps://dozenal.forumotion.com/t15-co-existing-baseshttps://dozenal.forumotion.com/t15-co-existing-baseswendy.kriegerNumbers are in a sense, transcriptions of stones on a stone-board. Regardless of the direction of writing, the largest columns are shown to the left, and the smallest to the right. The same order is preserved on calculators and cash registers. This is because most people are right-handed. When columns are divided to rows, the higher values are further away from the operator: the cash-registers run their numbers upwards, the stone-boards and abacuses run their rows with the units at the bottom.
The ...NumeralsSun, 18 Aug 2019 21:14:06 GMThttps://dozenal.forumotion.com/t15-co-existing-bases#50Names for base 12 and 18https://dozenal.forumotion.com/t12-names-for-base-12-and-18https://dozenal.forumotion.com/t12-names-for-base-12-and-18wendy.kriegerFor bases 12 and 18, the numbers past nine will be given in the form of excess+multiple of six,
dec 10 = foursix, dec 11 = fifsix. A proposal to call these 'mel' and 'lif' exists.
dec 12 = tulf, dec 13 = antulf dec 14 = twetulf, dec 15 = thirtulf, dec 16 = fourtulf, dec 17 = fiftulf.
For dozenal numbers, the names antig (onety), twentig, thirtig, etc to fifsixtig are used. After this, hundreds represent grosses, and thousands gross-of-grosses, in the style adopted for base 120. ...NomenclatureWed, 14 Aug 2019 21:39:17 GMThttps://dozenal.forumotion.com/t12-names-for-base-12-and-18#46Ripples and Awayness.https://dozenal.forumotion.com/t13-ripples-and-awaynesshttps://dozenal.forumotion.com/t13-ripples-and-awaynesswendy.kriegerRegular Numbers
Icarus at DozensOnline calls numbers whose prime divisors are in those of the base 'regular'. In the absense of any better word, I shall use the same here.
In decimal, the regular numbers are of the form \( 2^a 5^b \), In dozenal and base 18, these take the form \( 2^a 3^b \). The vast majority of regular numbers are multiples of the base, and so we eliminate all multiples of the base, leaving the 'regular mantissa'. The effect of this is to map 2, 20, 200, 2000, 20000 ...MathematicsWed, 14 Aug 2019 19:04:28 GMThttps://dozenal.forumotion.com/t13-ripples-and-awayness#45An Ounce of Timehttps://dozenal.forumotion.com/t14-an-ounce-of-timehttps://dozenal.forumotion.com/t14-an-ounce-of-timewendy.kriegerThe romans divided their units from the 'as' into a fraction-name which is most familiar with the weight system. An 'as' of weight is a pound, divided to 12 ounces, each of 8 drachms, of 3 scruples, of 6 siliqia (carats) of 4 grains. These serve also as ordinary fractions, such that '3 drachms' is 1/32 unit. The other unit that serves as a fraction is a clove or nail, being a digit of a foot, or 1/16. One finds 'nail of a yard', and 'nail of a hundredweight', representing the sixteenth part ...MetrologyWed, 14 Aug 2019 04:44:13 GMThttps://dozenal.forumotion.com/t14-an-ounce-of-time#40dm-kg systemhttps://dozenal.forumotion.com/t5-dm-kg-systemhttps://dozenal.forumotion.com/t5-dm-kg-systemwendy.kriegerIf you live in a metric country, and want to get to use dozenal, then this system gives you access to large numbers without too much trouble.
Counting does not really give you to really big numbers. This is why having good access to a ready source of simple numbers to convert is a good idea. We can use Wilberforce-Mann's names to distinguish these.
1. Time. Here we divide the day to 12 hours of 144 minutes of 144 seconds.
2. Length: LINN = 1 dm. Many of the values can easily be ...MetrologyTue, 13 Aug 2019 15:17:47 GMThttps://dozenal.forumotion.com/t5-dm-kg-system#39Pitman Numeralshttps://dozenal.forumotion.com/t7-pitman-numeralshttps://dozenal.forumotion.com/t7-pitman-numeralsPhaethonDozenal needs and has two more digits than the ten of decimal.
The Pitman character for ten is a turned digit two, ↊. The number of its Unicode code point or slot is 218A, where the letters A or B in a number suggest that this is a number written in the base four squared. It is derived from the initial letter t of the English word ten, but looks a little more like a Greek lower case letter tau, τ Unicode 03C4, in some styles or an insular half uncial style of the letter t, Ꞇ, that has ...NumeralsTue, 13 Aug 2019 12:58:23 GMThttps://dozenal.forumotion.com/t7-pitman-numerals#38Douze - notre dix futur [Essig, 1955]https://dozenal.forumotion.com/t11-douze-notre-dix-futur-essig-1955https://dozenal.forumotion.com/t11-douze-notre-dix-futur-essig-1955wendy.kriegerThis is an interesting text, it uses 7 for foursix, and 2 for fivesix.
The day is divided into 24 hours, of 12 dozenminutes, of 12 minutes, of 12 primes of 12 seconds. The example clock shows the hour and minute hands in the normal configuration, while the second hand is set on a second axle below the centre. This is in essence, the time system used in Pendlebury
The length units derive from the division of the earth-circle (ie great circle), 40,000 d km is ...ReferencesMon, 12 Aug 2019 08:44:53 GMThttps://dozenal.forumotion.com/t11-douze-notre-dix-futur-essig-1955#33