2d:null 2e:["$","title",null,{"children":"Egyptian numerals | Toph Tucker | Observable"}] 33:T4a6,md`# Egyptian numerals ##### 3300 bc – early first millennium ad ∙ [Wikipedia](https://en.wikipedia.org/wiki/Egyptian_numerals) ∙ [MacTutor](https://www-history.mcs.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html) ---

“Champollion deciphered the wrinkled granite hieroglyphics. But there is no Champollion to decipher the Egypt of every man’s and every being’s face.”

Herman Melville
Moby Dick

Hieroglyphs for powers of ten were concatenated in any direction, and their values were added. We think they represent a cattle hobble or horseshoe ${inlinePath( paths.get(10) )}, a coil of rope ${inlinePath( paths.get(100) )}, a lotus or water lily ${inlinePath( paths.get(1000) )}, a bent finger ${inlinePath( paths.get(10000) )}, a tadpole or possibly bird ${inlinePath( paths.get(100000) )}, and the god of infinity, Heh ${inlinePath( paths.get(1e6) )} — because apparently a million is close enough! ${quote( "cajori", 1, "bottom" )}`34:T1295,md`My “box-packing” layout of the individual marks here is sloppy; hieroglyphs of the same rank ought to be grouped, ordered from large to small, and in clusters of no more than four. Their spacing was better. In stone I guess these would be outlined. It is not at all clear to me when or how these were discovered or deciphered. It seems to predate the [Rosetta stuff](https://en.wikipedia.org/wiki/Rosetta_Stone). Did you know that it was Napoleon’s expeditionary army in Egypt that rediscovered it to Europe in 1799? That they had 167 art experts with them, to help with the, uh, looting? That Joseph Fourier — yes, he of the series and transforms! — pulled together a comprehensive publication of the findings? And that Napoleon inspected the Rosetta stone personally? And that an artist had to figure out how to use the stone as a printing block to get prints to scholars? Until Jean-François Champollion finally cracked it in 1822 by picking out phonetic characters for “Cleopatra”? It’s all very humbling, isn’t it, I know I should know more and be less surprised, but wow! Earlier examples of the hieroglyphic numerals feature very organic repetitions, with flowers sprouting from the same bush, as in this tally of enemies slain by a king circa 2800 BCE: ${quote( "ifrah1998", 0 )}

At first I was afraid that my SVG script was doing grievous harm to the forms by “rationalizing” them to mere mechanical side-by-side repetitions. But it turns out this just recapitulates (even heightens, advances!) the evolution of the hieroglyphics themselves, which became more standardized over the centuries. The numbers “276” and “4,622” show up as plunder tallies on the [Annals of Thutmosis III](https://www.louvre.fr/en/oeuvre-notices/annals-thutmosis-iii), over 1,300 years later; note the identically duplicated flowers: ${quote( "ifrah1998", 1 )}

The hieroglyphics evolved into the [hieratic](https://en.wikipedia.org/wiki/Hieratic) writing, a logographic cursive that mapped each of 1–9, 10–90, 100–900, 1000–9000 to a different symbol, ligating the repeated marks: ${quote( "ifrah1998", 2 )}

Compared to the hieroglyphs, it makes a familiar [space–time tradeoff](https://en.wikipedia.org/wiki/Space%E2%80%93time_tradeoff): more symbols to remember upfront; fewer strokes to draw a number. The [Moscow](https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus) (c. 1850 BC) and [Rhind](https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus) (c. 1550 BC) mathematical papyruses are written in it, and hieratic seems to have inspired the later [Greek numerals](https://observablehq.com/@tophtucker/greek-numerals), which mapped those same numbers onto the Greek alphabet. The Rhind papyrus includes several algebra problems; this one is labeled #34 (

) in the upper right, and reads right to left:

Cajori has a [detailed transcription](https://archive.org/details/historyofmathema031756mbp/page/n33) of the problem and its solution, translating step by step. ${quote( "cajori", 4 )} I won’t repeat him, and I can’t do it better, so it is worth looking at. Today it reads laboriously, like a notation in travail, not yet cleansed of dross — due mostly to hieratic only being able to represent unit fractions, i.e., reciprocals of integers, marked by a dot over the denominator, like

for ${tex`\frac{1}{7}`}. Also try to spot

, “heap”, working somewhat like our ${tex`x`} but not yet integrated as a full peer to the numbers. Today, for this problem, we might write: ${tex.block`\begin{aligned} \frac{x}{2} + \frac{x}{4} + x &= 10 \\ \left(\frac{1}{2} + \frac{1}{4} + 1\right)x &= 10 \\ \frac{7}{4}x &= 10 \\ x &= \frac{40}{7} \\ \end{aligned}`} `35:T1e77,sources = [ { date: -2800, alias: "Hieraconpolis statue", summary: "Shows the number of enemies slain by a king as a hieroglyphic “47,209”." }, { date: -1437, alias: "Annals of Thutmosis III", urls: ["https://www.louvre.fr/en/oeuvre-notices/annals-thutmosis-iii"], summary: "Shows hieroglyphic “276” and “4,622” as plunder tallies, with forms noticeably evolved from the Hieraconpolis statue." }, { date: -1850, alias: "Moscow mathematical papyrus", summary: "Written in the later hieratic numerals. Presents 25 mathematical problems, from arithmetic measuring the strength of beer to geometry computing the volume of a truncated pyramid or hemisphere; implies a value of π of about 3.16.", links: [ { label: "Wikipedia", url: "https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus" } ] }, { date: -1550, alias: "Rhind mathematical papyrus", summary: "Also written in hieratic; presents 91 problems in arithmetic, algebra, and geometry, including six on the slopes of the sides of pyramids. Also implies a value of π of about 3.16.", links: [ { label: "Wikipedia", url: "https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus" } ] }, { key: "rosetta", alias: "Rosetta stone", summary: "Includes some small numerals, including: ordinals for first, second, and third; the glyphs for “three” used as a pluralizing affix; and the glyph for “one” below a head for “per head”. The water lily appears to be overloaded with meanings other than a thousand.", urls: ["http://rosettastone.hieroglyphic-texts.net/sections/"], date: -196, links: [ { label: "Wikipedia", url: "https://en.wikipedia.org/wiki/Rosetta_Stone" }, { label: "British Museum", url: "https://www.britishmuseum.org/research/search_the_collection_database/search_object_details.aspx?objectid=117631&partid=1" } ] }, { key: "descriptiondelegypte", title: "Description de l’Égypte", date: 1809, authors: [ { name: "Joseph Fourier", role: "ed.", life: [1768, 1830], url: "https://en.wikipedia.org/wiki/Joseph_Fourier" } ], urls: ["https://archive.org/details/Descriptiondelq1Fran/page/n8"], summary: "Meticulous reports (including drawings and reproductions of glyphs) by Napoleon’s savants enabled the pursuit of Egyptology and decipherment by a distributed academic community." }, { key: "champollion", date: 1822, authors: [ { name: "Jean-François Champollion", life: [1790, 1832], url: "https://en.wikipedia.org/wiki/Jean-François_Champollion" } ], urls: [ "https://fr.wikisource.org/wiki/Lettre_à_M._Dacier_relative_à_l’alphabet_des_hiéroglyphes_phonétiques" ], title: "Lettre à M. Dacier", summary: "Champollion presented his breakthrough in cracking the Rosetta stone, arguing that the Egyptian writing mixed logographic and phonetic principles.", links: [ { label: "Wikipedia", url: "https://en.wikipedia.org/wiki/Lettre_à_M._Dacier" }, { label: "English translation", url: "https://en.wikipedia.org/wiki/File:Bryant_translation_Champollion_letter.pdf" } ] }, { key: "pihan", date: 1860, authors: [ { name: "Antoine Paulin Pihan", life: [1810, 1879], url: "https://fr.wikipedia.org/wiki/Antoine-Paulin_Pihan" } ], title: "Exposé des signes de numération", urls: ["https://archive.org/details/exposdessignesd00pihagoog/"], summary: "One of Cajori’s sources on Egyptian numeration. I include him because I am moved by the links in the chain of transmission who have fallen into obscurity." }, { key: "cajori", date: 1928, authors: [{ name: "Florian Cajori", life: [1859, 1930] }], title: "A History of Mathematical Notations", urls: ["https://archive.org/details/historyofmathema031756mbp"], summary: "Six pages of dense, comprehensive, encyclopedic material, including a reproduction and explanation of a hieratic algebraic problem from the Rhind papyrus.", quotes: [ [ "§16", "Of these the hieroglyphic has been traced back to about 3300 B.C.; it is found mainly on monuments of stone, wood, or metal. Out of the hieroglyphic sprang a more cursive writing known to us as hieratic. In the beginning the hieratic was simply the hieroglyphic in the rounded forms resulting from the rapid manipulation of a reed-pen as contrasted with the angular and precise shapes arising from the use of the chisel. About the eighth century B.C. the demotic evolved as a more abbreviated form of cursive writing. It was used since that time down to the beginning of the Christian Era. The important mathematical documents of ancient Egypt were written on papyrus and made use of the hieratic numerals." ], [ "§17", "The symbol for 1 represents a vertical staff; that for 1,000 a lotus plant; that for 10,000 a pointing finger; that for 100,000 a burbot; that for 1,000,000 a man in astonishment, or, as more recent Egyptologists claim, the picture of the cosmic deity Hh." ], [ "§19", "In applying the additive principle, not more than four symbols of the same kind were placed in any one group." ], [ "§20", "In the _older_ hieroglyphs 2,000 or 3,000 was represented by two or three lotus plants grown _in one bush_.… The later hieroglyphs simply place two lotus plants together, …without the appearance of springing from one and the same bush." ], [ "§23", "We reproduce an algebraic example in hieratic symbols, as it occurs in the most important mathematical document of antiquity known at the present time—the _Rhind papyrus_." ] ] }, { key: "ifrah1998", date: 1998, title: "The Universal History of Numbers: From Prehistory to the Invention of the Computer", authors: [{ name: "Georges Ifrah", life: [1947] }], location: "France", summary: "More narrative than Cajori, occasionally maligned in reviews I keep forgetting.", quotes: [ [ 165, "Another example of high numbers can be found on a statue from Hieraconpolis, dating from c. 2800 BCE, where the number of enemies slain by a king called KhaSeKhem are shown as 47,209 by the following signs… Figure 14.14 shows rather primitive features in the representation of the finger (= 10,000), the grouping of the thousands (lotus flowers) into two distinct sets, and the relatively poor alignment of the unit signs." ], [ 166, "From the Annals of Thutmosis (1490–1436 BCE), a list of the plunder of the twenty-ninth year of the Pharaoh’s reign" ], [ 170, "Hieratic script uses signs that are simplifications and schematisations of the corresponding hieroglyphs, with fewer details and with shapes reduced to skeleton forms. In some cases, the hieratic versions can be recognised as variants of the original sign; but most often the relationship between the “cursive” and the “monumental” form is impossible to guess and has to be learned sign by sign. ❡ There were also hieratic versions of the hieroglyphic numerals. These are the numerical signs found in the Harris Papyrus (British Museum), dating from the Twentieth Dynasty, which gives the possessions of the temples at the death of Ramses III (1192–1153 BCE):" ] ] } ]36:Ta69,paths = new Map([ [1, "M1 0V35"], [ 10, "M1 35V13.0506C1 13.0506 1 1 14.0781 1C27.1562 1 28 13.0506 28 13.0506V35" ], [ 100, "M16.9651 36C16.9651 36 1 19.2955 1 10.9432C1 2.5909 6.58778 1 10.1799 1C14.2713 0.999994 17.3655 4.8971 16.9651 8.95455C16.6813 11.8298 15.474 14.9205 12.5747 14.9205C7.78517 14.9205 7.78517 8.95455 7.78517 8.95455" ], [ 1000, "M12.5 65.5C15.5 65.5 17.5 69 17.5 69M12.5 65.5C9.5 65.5 7.5 69 7.5 69M12.5 65.5C12.5 47.3406 12.5 37.1594 12.5 19M17.5 69L24.5 79H1L7.5 69M17.5 69L24.5 61M7.5 69L1 61M12.5 19C5.5 17.6891 1 13.5 1 10C1 6.5 7 1 12.5 1C18 1 21.5 4.5 21.5 4.5L14.5 10L21.5 15C21.5 15 16.5 19.5 12.5 19Z" ], [ 10000, "M16 0.999988C18.5 1.99999 17.5 7.99999 16.5 9.99999C15.5 12 12.5 23.5 11.5 31.5C10.5 39.5 12 77 10 79C8 81 1.5 80.5 1.5 80.5C1.5 80.5 2 35 3 28.5C4 22 5.5 14.5 6.5 11M16 0.999988C11.5 -0.800014 7.5 7.49999 6.5 11M16 0.999988C15 9 11 12 6.5 11" ], [ 100000, "M1 8.5C1 8.5 4.1986 3.52799 9.5 1.49999C20 -2.51669 25.5 10.5 39.5 18.5C50.7521 24.9298 53.2203 33.1039 57 45.5C60.6519 57.4768 60 79 60 79C60 79 52 50 45.5 43M1 8.5C1 8.5 8.73359 8.37 10.8419 11C12.9502 13.63 15.7973 21.5 15.7973 21.5M1 8.5C1 8.5 6.56449 11.4719 10.8419 15.2072C11.0651 15.4021 11.2848 15.5991 11.5 15.7979C12.4479 16.6733 13.309 17.5829 14 18.5C14.7676 19.5187 15.3426 20.5143 15.7973 21.5M35 27C35 27 27.8333 31.5 30.5 39.5C33.1667 47.5 48.5142 47.5 48.5142 47.5C44.398 47.9078 32.1607 47.373 29 45.5C23.9605 42.5136 22.8949 38.5925 20 33.5C17.5124 29.124 17.5917 25.3899 15.7973 21.5" ], [ 1000000, "M22.5 36H11.5L3 9H0.5M22.5 36C22.5 36 26.8944 42.005 28 46.5C29.5149 52.6593 26.5 64 26.5 64M22.5 36L24 32M43.5 36H55.5L61 9H63.5M43.5 36C43.5 36 39.88 42.1264 39 46.5C38.1526 50.7114 39 57.5 39 57.5M43.5 36L41 34M1 81.5C1 81.5 37 77 41 78.5C45 80 45 81.5 45 81.5H50L39 73.5M1 81.5L39 73.5M1 81.5L26.5 64M39 73.5V57.5M39 57.5L26.5 64M26.5 64C26.5 64 13.6298 54.9489 7.77198 50M7.77198 50C7.77198 58.6989 7.77198 76.5 7.77198 76.5C7.77198 76.5 2.325 53.85 3.5 51.5C4.675 49.15 5.5 49 7.77198 50ZM22.5 24.5C23 20.5 27 17 27 17M22.5 24.5C22 28.5 24 32 24 32M22.5 24.5C24 26 25.3325 25.5378 26.5 24.5C27.7426 23.3954 27 17 27 17M31 16C35 16 41 18.5 41 23M31 16C28 16 27 17 27 17M31 16C31 13.5592 31 9.75 31 9.75M41 23C41 27.2958 41 34 41 34M41 23C39.9519 27.5214 39.7574 29.7042 38 34M41 34C41 34 39.7574 34 38 34M27 17C27 17 29.5164 20.2852 30.5 22C31.5687 23.8631 31 28.5 31 28.5M38 34C36.8284 36.1479 35 39.5 35 39.5C35 39.5 31.976 35.8108 31.5 33.5C31.0667 31.3963 31 28.5 31 28.5M31 28.5L24 32M31 3.5C31 0.5 35 0.5 35 0.5M31 3.5V9.75M31 3.5L28 5.5L31 9.75" ] ])37:[] 31:{"id":"e24acaf59998c085","slug":"egyptian-numerals","title":"Egyptian numerals","thumbnail":"89a622dd075268ad1e88c1d2065c2efbfe0d766d958cd7d03a5539e4fb706fc2","access_level":"public","create_time":"$D2019-08-26T17:24:18.761Z","update_time":"$D2023-05-26T08:48:34.570Z","view_time":null,"first_public_time":"$D2019-11-02T07:12:38.576Z","fork":false,"stars":17,"starred":false,"owner":{"type":"team","id":"97290e936c339d8e","login":"tophtucker","name":"Toph Tucker","avatar_url":"https://avatars-next.observableusercontent.com/3706c31a8f9c59bb716c022c04b9c073144cd1368b78ac85f49139be6c93c34e","tier":"pro_2024"},"version":1120,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"0bb2842b01e0c652","login":"tophtucker","name":"Toph Tucker","avatar_url":"https://avatars-next.observableusercontent.com/3706c31a8f9c59bb716c022c04b9c073144cd1368b78ac85f49139be6c93c34e","tier":null}],"members":[{"type":"individual","id":"0bb2842b01e0c652","login":"tophtucker","name":"Toph Tucker","avatar_url":"https://avatars-next.observableusercontent.com/3706c31a8f9c59bb716c022c04b9c073144cd1368b78ac85f49139be6c93c34e","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":{"id":"d40cc4f153f404b4","slug":"how-we-do-math","title":"How We Do Math","owner":{"id":"97290e936c339d8e","login":"tophtucker","name":"Toph Tucker"}},"type":"notebook","body":{"title":"Egyptian numerals","cells":[{"id":267,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":447,"value":"html`

${Array.from(digits.values()).map(\n (d, i) => svg``\n)}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":237,"value":"md`So ${tex`${Math.floor(10 ** n)}`} would be written something like:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"viewof n = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"html`

${numToEgyptian(Math.floor(10 ** n))}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":341,"value":"md`There were a couple special glyphs for common fractions — ${inlinePath(\n half\n)} for ${tex`\\frac{1}{2}`}, ${inlinePath(\n twothirds\n)} for ${tex`\\frac{2}{3}`} — but beyond that, the hieroglyphs could only represent unit fractions, i.e. reciprocals of integers, whereas we can write any number over any other number. (They got there by [adding unit fractions](https://en.wikipedia.org/wiki/Egyptian_fraction).) Unit fractions were written with the integer under the oval mouth-like hieroglyph ${inlinePath(\n solidus\n)}, so ${tex`\\frac{1}{${Math.floor(\n 10 ** n2\n)}}`} would be written something like:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":350,"value":"viewof n2 = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":346,"value":"html`

${numToEgyptianFraction(\n Math.floor(10 ** n2)\n)}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":0,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":929,"value":"md`---\n\n#### Source chronology`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":621,"value":"bibliography(sources)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":618,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1102,"value":"md`\n

“Les princes et les chefs de l’armée égyptienne conduisent au roi victorieux quatre colonnes de prisonniers; des scribes comptent et enregistrent le nombre des mains droites et des parties génitales coupées aux Robou morts sur le champ de bataille.”

Jean-François Champollion
Letter from Thebes, 1829

\n\n---\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":616,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":818,"value":"quote = quoter(sources)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":532,"value":"inlinePath = (path, height = 16) => {\n const resized = size(undefined, height)(path);\n const { width } = getBBox(resized);\n return svg``;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"digits = new Map(\n Array.from(paths.entries()).map(([value, path], i) => {\n const bbox = bboxs[i];\n return [\n value,\n {\n value,\n path,\n w: bbox.w,\n h: bbox.h\n }\n ];\n })\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":302,"value":"solidus = \"M57.5 0.500001C33.971 0.320745 0 18.5 0 18.5C0 18.5 34.0846 35.6702 57.5 35.5C80.3542 35.3339 113.5 18.5 113.5 18.5C113.5 18.5 80.4707 0.675003 57.5 0.500001Z\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1061,"value":"half = \"M18 0.5H54L58 6H21L11 23H54L52 28.5H1L18 0.5Z\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1073,"value":"twothirds = \"M18.7445 11.9996C26.1948 11.9426 37 6.17143 37 6.17143C37 6.17143 26.2327 0.0604479 18.7445 0.00045151C11.0742 -0.0610032 0 6.17143 0 6.17143C0 6.17143 4.08345 8.33474 9 10.0255M18.7445 11.9996C15.7387 12.0225 12.1936 11.1237 9 10.0255M18.7445 11.9996V21.5M9 10.0255V16\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"bboxs = {\n const margin = 1;\n const nodes = renderings.querySelectorAll(\"path\");\n return Array.from(nodes).map(node => {\n const bb = node.getBBox();\n return { w: bb.width + margin, h: bb.height + margin };\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"numToEgyptianDigits = n => {\n const arr = [];\n let m = n;\n while (m) {\n let d = ranks.find(d => d <= m);\n arr.push(d);\n m -= d;\n }\n return arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":900,"value":"numToEgyptianPath = n => {\n const margin = 5;\n const d = d3\n .merge(\n Array.from(\n d3array.group(numToEgyptianDigits(n), d => d).values()\n ).map(d => (d.length > 4 ? chunks(d, 3) : [d]))\n )\n .map(d => {\n const { path, w, h } = digits.get(d[0]);\n return {\n path: combine(d.map((_, i) => translate(i * (w + margin), 0)(path))),\n w: d.length * (w + margin) + margin,\n h: h + margin\n };\n });\n potpack(d);\n // or do `const { w, h } = potpack(d)` to save computed dimensions and not have to get bbox\n return combine(d.map(({ path, x, y }) => translate(x, y)(path)));\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1014,"value":"numToEgyptian = n => {\n const path = scale(0.7)(numToEgyptianPath(n));\n const { width, height } = getBBox(path);\n return svg``;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":396,"value":"numToEgyptianFraction = n => {\n const scaleFactor = 0.7;\n const path = scale(scaleFactor)(center(numToEgyptianPath(n)));\n const { width, height } = getBBox(path);\n\n const solidusScaleFactor = 0.4;\n const solidusPath = scale(solidusScaleFactor)(center(solidus));\n const solidusBBox = getBBox(solidusPath);\n const w = solidusBBox.width;\n const h = solidusBBox.height;\n\n const svgWidth = Math.max(width, w);\n const marginBetween = 3;\n\n return svg``;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"ranks = Array.from(paths.keys()).sort((a, b) => b - a)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"d3 = require(\"d3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":876,"value":"d3array = require(\"d3-array\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":87,"value":"potpack = (await import('https://unpkg.com/potpack@2.0.0/index.js?module')).default","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":298,"value":"import { bibliography, quoter, chunks, epigraph } from \"@tophtucker/scrapbook\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":515,"value":"import {\n translate,\n scale,\n size,\n combine,\n center,\n normalizeHV,\n getBBox\n} from \"@tophtucker/pathstuff\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":71,"value":"html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1108,"value":"epigraph","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"renderings = svg``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":278,"value":"todo = md`#### Todo:\n- SVG hieratic?\n- Add numeric input to slider\n- Use getBBox so I don’t need to draw the glyphs to measure them\n- https://twitter.com/SumerianHittite/status/1404287227966939138/photo/1`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1","titling":"auto"}} 32:"$31:body"