Base Dozen Forumhttps://dozenal.forumotion.com/feed/?Latest topicsfrSat, 07 Sep 2024 19:10:35 GMT10Base Dozen Forumhttps://illiweb.com/fa/m/logo3.gifhttps://dozenal.forumotion.com/feed/?Continued Fraction Constantshttps://dozenal.forumotion.com/t69-continued-fraction-constantshttps://dozenal.forumotion.com/t69-continued-fraction-constantsPhaethonAll real numbers can be written as continued fractions independently of any base of positional notation. The Lévy constant arises from the co-efficients of most continued fractions and is explained on Wikipedia. It is: \( e^{\frac {\pi^2}{12 \ln{2}} } \). As can be seen, it contains the number twelve.
Related to the Lévy constant are the Lochs constants, which also apply to most continued fractions but depend on the base of enumeration. For base \(B\), the Lochs constant is \( \frac{6 \ln{2} ...MathematicsSat, 07 Sep 2024 19:10:35 GMThttps://dozenal.forumotion.com/t69-continued-fraction-constants#220Twelve Metal Colossal Statueshttps://dozenal.forumotion.com/t68-twelve-metal-colossal-statueshttps://dozenal.forumotion.com/t68-twelve-metal-colossal-statuesPhaethonThe first emperor of China, Shi Huang Di, who established standards of weights and measures, ordered the bronze weapons of those he conquered to be cast into twelve enormous statues.
This can be interpreted as a message of converting war into celebration of peace, similar to the story for the creation of the colossus of Rhodes.
Is it possible that the apparently megalomaniac emperor had dozenist tendencies?
References:
https://en.wikipedia.org/wiki/Twelve_Metal_Colossi
https://en.wikipedia.org/wiki/Colossus_of_Rhodes
PhaenomenaMon, 02 Sep 2024 15:48:49 GMThttps://dozenal.forumotion.com/t68-twelve-metal-colossal-statues#219Dozenal Pointhttps://dozenal.forumotion.com/t67-dozenal-pointhttps://dozenal.forumotion.com/t67-dozenal-pointPhaethonTwo ways of representing rational numbers between integers are as
vulgar fractions in the form A/B by one integer A divided by another B and
in positional notation by numerals after a punctuation mark between them and the integer part.
When the base of enumeration is ten,
the numerals after the integer part are called decimals to distinguish them from vulgar fractions and
the punctuation mark is called the decimal point in English.
When the base of enumeration is twelve, the numerals ...NomenclatureThu, 29 Aug 2024 13:01:44 GMThttps://dozenal.forumotion.com/t67-dozenal-point#218Quantum Mechanics and the Principle of Least Radix Economyhttps://dozenal.forumotion.com/t66-quantum-mechanics-and-the-principle-of-least-radix-economyhttps://dozenal.forumotion.com/t66-quantum-mechanics-and-the-principle-of-least-radix-economyPhaethonSelected quotations and author highlights:
[Page 2, Section 1, Introduction] wrote:"nature makes dynamically the most effective choice for the radix in which its computations take place."
[Page 2, Section 1, Introduction] wrote:"By demanding that this radix works most efficiently physical laws are derived in a unified way."
[Page 5, Section 2, Radix economy and the Lagrangian action] wrote:"matrix representation characterizes each number in each radix in ...ReferencesSat, 29 Jun 2024 16:15:46 GMThttps://dozenal.forumotion.com/t66-quantum-mechanics-and-the-principle-of-least-radix-economy#214Phonetic Dozenal Number Nameshttps://dozenal.forumotion.com/t65-phonetic-dozenal-number-nameshttps://dozenal.forumotion.com/t65-phonetic-dozenal-number-namesPhaethonTitle: Phonetic Dozenal Number Names
Subtitle: Words for Twelve Numbers Constructed A Priori
To construct words for dozenal numbers logically, twelve numbers would be formed out of as many contrastive features as are necessary to distinguish them from each other. To distinguish twelve items, the quickest way is by two binary contrasts and one ternary contrast. Every word must be one syllable long at a minimum. Since the smallest possible syllable consists of one nucleus or monophthongal vowel, ...NomenclatureSun, 14 Apr 2024 23:08:41 GMThttps://dozenal.forumotion.com/t65-phonetic-dozenal-number-names#213Dozenal Number Words from Metric Prefixeshttps://dozenal.forumotion.com/t64-dozenal-number-words-from-metric-prefixeshttps://dozenal.forumotion.com/t64-dozenal-number-words-from-metric-prefixesPhaethonIn the decimal metric prefixes, there are deci- for a fractional tenth and deca- for ten. These imply a common morpheme dec for ten and variation of the vowel to -a- for a positive exponent and to -i- for a negative exponent or reciprocal.
For the purpose of a dozenal derivation of numbers, I decide to interpret these metric prefixes differently. The syllables -ca- and -ci- are considered to represent twelve and its reciprocal respectively, while the syllable de is considered to be derived ...NomenclatureSat, 13 Apr 2024 14:38:34 GMThttps://dozenal.forumotion.com/t64-dozenal-number-words-from-metric-prefixes#212Dozenalizing 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, 05 Apr 2024 11:23:41 GMThttps://dozenal.forumotion.com/t3-dozenalizing-metric#210Myon 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 ...NomenclatureSat, 17 Feb 2024 15:18:22 GMThttps://dozenal.forumotion.com/t25-myon-dozenal-nomenclature#209Information per Area of Numerical Formshttps://dozenal.forumotion.com/t62-information-per-area-of-numerical-formshttps://dozenal.forumotion.com/t62-information-per-area-of-numerical-formsPhaethonTitle: Information per Area of Numerical Forms
Subtitle: Quantifying the Compactness of Symbolisation for Bases
Recently (①⑥th December ①②⓪⑦) on the DozensOnline website forum, a video on binary as a better base than base six or decimal was linked to. In chapter zero of that video, the following claim was narrated:
kepe wrote:"Maybe the problem isn't with binary itself but with a specific notation of binary. [...] The most common choice are [sic] the ...NumeralsMon, 29 Jan 2024 10:50:52 GMThttps://dozenal.forumotion.com/t62-information-per-area-of-numerical-forms#208Denominational Dozenal Numeralshttps://dozenal.forumotion.com/t63-denominational-dozenal-numeralshttps://dozenal.forumotion.com/t63-denominational-dozenal-numeralsPhaethonTitle: Denominational Dozenal Numerals
Subtitle: Rationally Designed Base Twelve Figures
This month, I discovered a video containing dozenal numerals. A transcript of excepts from the video follows:
Gosia Duszak wrote:[13:03] "Another day. Originally in Spanish, 2020, exact date unknown."
[...]
"Math is totally different, starting from how we write it, so I have to begin like in kindergarten. Look, this is one, and this is two."
[...]
[13:41] "in base twelve, there is no zero ...NumeralsSun, 28 Jan 2024 21:25:55 GMThttps://dozenal.forumotion.com/t63-denominational-dozenal-numerals#207Proto-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 ...NomenclatureFri, 12 Jan 2024 16:25:46 GMThttps://dozenal.forumotion.com/t26-proto-indo-european-numbers#204Radix Economy for Alternating Baseshttps://dozenal.forumotion.com/t61-radix-economy-for-alternating-baseshttps://dozenal.forumotion.com/t61-radix-economy-for-alternating-basesPhaethonTitle: Radix Economy for Alternating Bases
Subtitle: Efficiency of Bases for Specifying Information
Introduction:
As a way of quantifying the cost of increasing the size of a base, radix economy is often mentioned. I will derive a definition for a version of radix economy from the number of options from which to select required to specify a piece of information or datum by a numerical base. To specify a piece of information, a sequence of questions must be answered with the number of options ...MathematicsSun, 24 Dec 2023 17:41:44 GMThttps://dozenal.forumotion.com/t61-radix-economy-for-alternating-bases#199Graduation 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 ...MetrologySat, 02 Dec 2023 12:58:12 GMThttps://dozenal.forumotion.com/t47-graduation-subdivisions#198Pendulum 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 ...MetrologySat, 07 Oct 2023 20:22:01 GMThttps://dozenal.forumotion.com/t23-pendulum-system#197Colour Classificationhttps://dozenal.forumotion.com/t55-colour-classificationhttps://dozenal.forumotion.com/t55-colour-classificationPhaethonIntroduction: Motivation in Connection with Dozenism
One application for base twelve where a division by three is thought to be convenient is in the classification of colour hues with reference to the three pigments of trichromatism. A representation of all the possible hues can be depicted in a planar cross-section through a three-dimensional space in which all colours can be plotted, for example by using as co-ordinates the amounts of three primary colours, most typically Red (R), Green (G), ...PhaenomenaSat, 07 Oct 2023 18:16:22 GMThttps://dozenal.forumotion.com/t55-colour-classification#196Unit Power Prefixeshttps://dozenal.forumotion.com/t57-unit-power-prefixeshttps://dozenal.forumotion.com/t57-unit-power-prefixesPhaethonWhile it is possible to talk about dozenal numbers entirely in the English language without having to invent any new words, and I do not believe that a new language in the style of arbitrary natural languages should be fabricated as a replacement for English or other natural languages when discussing numbers in base twelve in ordinary conversation or written discourse, in terms of how many words and letters would be required to represent a number, the natural English language would not always ...NomenclatureThu, 05 Oct 2023 16:29:01 GMThttps://dozenal.forumotion.com/t57-unit-power-prefixes#195How a Dozenal Metrological System Should be Developedhttps://dozenal.forumotion.com/t60-how-a-dozenal-metrological-system-should-be-developedhttps://dozenal.forumotion.com/t60-how-a-dozenal-metrological-system-should-be-developedPhaethonHow a Dozenal Metrological System Should be Developed
The design of a system of measure with relationships between its units based on twelve should be designed by applying well chosen principles from the outset. Before the units are defined, the type of metrological system should be decided upon for the features that are desirable, useful, and prone to being adopted out of necessity or convenience. There are two strategies that have merit for the basis of a metrological system, as follows:
A ...MetrologyTue, 05 Sep 2023 19:33:46 GMThttps://dozenal.forumotion.com/t60-how-a-dozenal-metrological-system-should-be-developed#192Optimal 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, 02 Jul 2023 16:10:59 GMThttps://dozenal.forumotion.com/t46-optimal-analogue-clock#191Dozenal 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 ...MathematicsTue, 13 Jun 2023 22:00:50 GMThttps://dozenal.forumotion.com/t24-dozenal-fifths-better-than-decimal-thirds#190Old School Textbook Duodecimalhttps://dozenal.forumotion.com/t59-old-school-textbook-duodecimalhttps://dozenal.forumotion.com/t59-old-school-textbook-duodecimalPhaethonToday I discovered didactic text on base twelve that I had not noticed before in an old school mathematics textbook. A facsimile of one such page is shown in the following image:
Facsimile of Page 36, New Intermediate Mathematics
The text mentions the greater likelihood of base twelve replacing decimal, extant use of base twelve in real practical spatial measurement computations, the ordinary English words dozen and gross for powers of twelve, some benefits of base twelve, that the extra ...PhaenomenaSun, 02 Apr 2023 21:59:46 GMThttps://dozenal.forumotion.com/t59-old-school-textbook-duodecimal#187Perpetual Calendarhttps://dozenal.forumotion.com/t58-perpetual-calendarhttps://dozenal.forumotion.com/t58-perpetual-calendarPhaethonSome dozenists have contributed considerable effort on how the calendar can be regularised. At the moment, on the DozensOnline website forum, there is discussion of conventional perpetual calendars and a one page calendar. The photograph of the following item utilises a perpetual calendar based on the same principles:
Photograph of Perpetual Calendar Fob
I acquired this item as a curiosity and have not been using it practically since it is more convenient to check the day on an electronic ...PhaenomenaTue, 14 Mar 2023 12:54:58 GMThttps://dozenal.forumotion.com/t58-perpetual-calendar#186Potencyhttps://dozenal.forumotion.com/t54-potencyhttps://dozenal.forumotion.com/t54-potencyPhaethonTitle: Potency
Subtitle: Informational Efficacy of Symbolisation to Exponentiated Bases
Introduction: Positional Notation
In positional numerical notation, we are used to as many different and distinguishable symbols in a set or inventory of characters as the cardinal number of the base to the first power being available for each place or position representing any power of that base. In this case, the number of items, say \(N\), that may be referred to as numbers, names, or words by a set ...MathematicsMon, 27 Feb 2023 17:48:38 GMThttps://dozenal.forumotion.com/t54-potency#182Mnemonicshttps://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 ...NomenclatureTue, 07 Feb 2023 17:43:32 GMThttps://dozenal.forumotion.com/t27-mnemonics#177Dozenal Roman Numeralshttps://dozenal.forumotion.com/t56-dozenal-roman-numeralshttps://dozenal.forumotion.com/t56-dozenal-roman-numeralsPhaethonIn the topic on graduation divisions for measurement scales at Base Dozen Forum, Metrology, Graduation Subdivisions, the proposal today in the third post there almost suggests specification of marks on the scale by additive and subtractive denominational numerals like Roman numerals but in base twelve, as follows:
Code:
| | | | | | | | | | | | |
| | | | | | | | |
| | | | |
| ...NumeralsTue, 17 Jan 2023 15:18:30 GMThttps://dozenal.forumotion.com/t56-dozenal-roman-numerals#175Pasigraphie 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#156Dozenal 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:
<br />
<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#150Troyhttps://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#132Dozenal 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#127Tableshttps://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#123