Chuck Jones’ The Dot and the Line Celebrates Geometry & Hard Work: An Oscar-Winning Animation (1965)

The ani­mat­ed short above, The Dot and the Line, direct­ed by the great Chuck Jones and nar­rat­ed by Eng­lish actor Robert Mor­ley, won an Oscar in 19656 for Best Ani­mat­ed Short Film. Based on a book writ­ten by Nor­ton Juster, “The Dot and the Line” tells the sto­ry of a romance between two geo­met­ric shapes—taking the arche­typ­al nar­ra­tive tra­jec­to­ry of boy meets girl, los­es girl, wins girl in the end (find­ing him­self along the way) and inject­ing it with some fas­ci­nat­ing social com­men­tary that still res­onates almost fifty years lat­er. One way of watch­ing “The Dot and the Line” is as a “tri­umph of the nerd” sto­ry, where an anx­ious square (as in “uncool”) Line has to com­pete with a hip­ster beat­nik Squig­gle of a rival for the affec­tions of a flighty Dot.

The Line begins the film “stiff as a stick… dull, con­ven­tion­al and repressed” (as his love inter­est says of him) in con­trast to the groovy Squig­gle and his groovy bebop sound­track. With the pos­si­ble sug­ges­tion that this love trans­gress­es mid-cen­tu­ry racial bound­aries, the Line’s friends dis­ap­prove and tell him to give it up, since “they all look alike any­way.” But the Line per­sists in his fol­ly, indulging in some Wal­ter Mit­ty-like rever­ies of hero­ic endeav­ors that might win over his Dot. Final­ly, using “great self-con­trol,” he man­ages to bend him­self into an angle, then anoth­er, then a series of sim­ple, then very com­plex, shapes, becom­ing, we might assume, some kind of math­e­mat­i­cal wiz. After refin­ing his tal­ents alone, he goes off to show them to Dot, who is “over­whelmed” and delight­ed and who “gig­gles like a school­girl.”

Here the sub­text of the nerd-gets-the-girl sto­ry­line man­i­fests a fair­ly con­ser­v­a­tive cri­tique of the “anar­chy” of the Squig­gle, whom the Dot comes to see as “undis­ci­plined, grace­less, coarse” and oth­er unflat­ter­ing adjec­tives while the line—who pro­claimed to him­self ear­li­er that “free­dom is not a license for chaos”—is “daz­zling, clever, mys­te­ri­ous, ver­sa­tile, light, elo­quent, pro­found, enig­mat­ic, com­plex, and com­pelling.” I can almost imag­ine that George Will had a hand in the writ­ing, which is to say that it’s enor­mous­ly clever, and enor­mous­ly invest­ed in the val­ues of self-con­trol, hard work, and dis­ci­pline, and dis­trust­ful of spon­tane­ity, free play, and gen­er­al groovi­ness. At the end of the film, our Dot and Line go off to live “if not hap­pi­ly ever after, at least rea­son­ably so” in some cozy sub­urb, no doubt. The moral of the sto­ry? “To the vec­tor belong the spoils.”

If you would like to sup­port the mis­sion of Open Cul­ture, con­sid­er mak­ing a dona­tion to our site. It’s hard to rely 100% on ads, and your con­tri­bu­tions will help us con­tin­ue pro­vid­ing the best free cul­tur­al and edu­ca­tion­al mate­ri­als to learn­ers every­where. You can con­tribute through Pay­Pal, Patre­on, and Ven­mo (@openculture). Thanks!

Relat­ed Con­tent 

Carl Sagan Explains Evo­lu­tion in an 8‑Minute Ani­ma­tion

Watch “Geom­e­try of Cir­cles,” the Abstract Sesame Street Ani­ma­tion Scored by Philip Glass (1979)

Jour­ney to the Cen­ter of a Tri­an­gle: Watch the 1977 Dig­i­tal Ani­ma­tion That Demys­ti­fies Geom­e­try

Josh Jones is a writer and musi­cian based in Durham, NC. 

RIP Gladys Mae West, the Pioneering Black Mathematician Who Helped Lay the Foundation for GPS

Gladys Mae West was born in rur­al Vir­ginia in 1930, grew up work­ing on a tobac­co farm, and died ear­li­er this month a cel­e­brat­ed math­e­mati­cian whose work made pos­si­ble the GPS tech­nol­o­gy most of us use each and every day. Hers was a dis­tinc­tive­ly Amer­i­can life, in more ways than one. Seek­ing an escape from the agri­cul­tur­al labor she’d already got­ten to know all too well, she won a schol­ar­ship to Vir­ginia State Col­lege by becom­ing her high school class vale­dic­to­ri­an; after earn­ing her bach­e­lor’s and mas­ter’s degrees in math­e­mat­ics, she taught for a time and then applied for a job at the naval base up in Dahlgren. She first dis­tin­guished her­self there by ver­i­fy­ing the accu­ra­cy of bomb­ing tables with a hand cal­cu­la­tor, and from there moved on up to the com­put­er pro­gram­ming team.

This was the ear­ly nine­teen-six­ties, when pro­gram­ming a com­put­er meant not cod­ing, but labo­ri­ous­ly feed­ing punch cards into an enor­mous main­frame. West and her col­leagues used IBM’s first tran­sis­tor­ized machine, the 7030 (or “Stretch”), which was for a few years the fastest com­put­er in the world.

It cost an equiv­a­lent of $81,860,000 in today’s dol­lars, but no oth­er com­put­er had the pow­er to han­dle the project of cal­cu­lat­ing the pre­cise shape of Earth as affect­ed by grav­i­ty and the nature of the oceans. About a decade lat­er, anoth­er team of gov­ern­ment sci­en­tists made use of those very same cal­cu­la­tions when putting togeth­er the mod­el employed by the World Geo­det­ic Sys­tem, which GPS satel­lites still use today. Hence the ten­den­cy of cel­e­bra­to­ry obit­u­ar­ies to under­score the point that with­out West­’s work, GPS would­n’t be pos­si­ble.

Nor do any of them neglect to point out the fact that West was black, one of just four such math­e­mati­cians work­ing for the Navy at Dahlgren. Sto­ries like hers have drawn much greater pub­lic inter­est since the suc­cess of Hid­den Fig­ures, the Hol­ly­wood adap­ta­tion of Mar­got Lee Shet­ter­ly’s book about the black female math­e­mati­cians at NASA dur­ing the Space Race. When that movie came out, in 2016, even West­’s own chil­dren did­n’t know the impor­tance of the once-clas­si­fied work she’d done. Only in 2018, when she pro­vid­ed that infor­ma­tion on a bio­graph­i­cal form she filled out for an event host­ed by her col­lege soror­i­ty, did it become pub­lic. She thus spent the last years of her long life as a celebri­ty, sought out by aca­d­e­mics and jour­nal­ists eager to under­stand the con­tri­bu­tions of anoth­er no-longer-hid­den fig­ure. But to their ques­tions about her own GPS use, she report­ed­ly answered that she pre­ferred a good old-fash­ioned paper map.

Relat­ed con­tent:

Mar­garet Hamil­ton, Lead Soft­ware Engi­neer of the Apol­lo Project, Stands Next to Her Code That Took Us to the Moon (1969)

Women’s Hid­den Con­tri­bu­tions to Mod­ern Genet­ics Get Revealed by New Study: No Longer Will They Be Buried in the Foot­notes

Meet Grace Hop­per, the Pio­neer­ing Com­put­er Sci­en­tist Who Helped Invent COBOL and Build the His­toric Mark I Com­put­er (1906–1992)

Joce­lyn Bell Bur­nell Dis­cov­ered Radio Pul­sars in 1974, But the Cred­it Went to Her Advi­sor; In 2018, She Gets Her Due, Win­ning a $3 Mil­lion Physics Prize

Hen­ri­et­ta Lacks Gets Immor­tal­ized in a Por­trait: It’s Now on Dis­play at the Nation­al Por­trait Gallery

Black His­to­ry in Two Min­utes: Watch 93 Videos Writ­ten & Nar­rat­ed by Hen­ry Louis Gates Jr.

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. He’s the author of the newslet­ter Books on Cities as well as the books 한국 요약 금지 (No Sum­ma­riz­ing Korea) and Kore­an Newtro. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

The Ancient Tool Used in Japan to Strengthen Memory & Focus: The Abacus

William Gib­son famous­ly observed that the future is already here, it’s just not even­ly dis­trib­uted. That line is often thought to have been inspired by Japan, which was already pro­ject­ing a thor­ough­ly futur­is­tic image, at least in pop­u­lar cul­ture, by the time he made his debut with Neu­ro­mancer in 1984. But as any­one who’s spent enough time in the coun­try under­stands — albeit not with­out frus­tra­tion — even twen­ty-first-cen­tu­ry Japan remains in many ways a pre-dig­i­tal soci­ety. Many busi­ness­es only take cash, more than a few ser­vices require com­mu­ni­ca­tion by fax, and there’s no sub­sti­tute for a phys­i­cal han­ko seal on impor­tant doc­u­ments. Even so, it may come as a sur­prise to learn that Japan still uses aba­cus­es.

Or rather, Japan still uses aba­cus­es as edu­ca­tion­al tools: you won’t see many shop­keep­ers pull them out while ring­ing up your pur­chas­es, but if you glance in the win­dow of the right kind of pri­vate acad­e­my, you might well see young stu­dents furi­ous­ly per­form­ing cal­cu­la­tions the very old-fash­ioned way.

If they’re suf­fi­cient­ly advanced, as explained in the BBC video above, they won’t even have actu­al aba­cus­es; they’ll just move around beads pic­tured in their heads. (It brings to mind how Dustin Hoff­man’s savant in Rain Man explains his per­for­mance of seem­ing­ly impos­si­ble men­tal math: “I see it.”) Such inten­sive aba­cus edu­ca­tion was com­mon across north­east Asia in the mid-twen­ti­eth cen­tu­ry, when the arith­metic skills it cul­ti­vat­ed were impor­tant for both indi­vid­ual sur­vival and nation­al devel­op­ment.

It was that very devel­op­ment that tend­ed to push the aba­cus into obso­les­cence. When Korea, where I live, could afford elec­tron­ic cal­cu­la­tors, the pres­tige asso­ci­at­ed with aba­cus mas­tery dis­solved prac­ti­cal­ly overnight. Deter­mined Kore­an par­ents can still sign their chil­dren up for jupan class­es, much as Chi­nese par­ents might encour­age theirs to enter into suan­pan com­pe­ti­tions out of a sense of civ­i­liza­tion­al pride, but they have noth­ing like the sta­tus the soroban enjoys in Japan. That may be vin­di­cat­ed by neu­ro­sci­en­tif­ic research point­ing toward the ben­e­fits learn­ing the aba­cus can have on a devel­op­ing brain’s cog­ni­tive func­tions. As the BBC video explains, aba­cus train­ing enhances cog­ni­tive func­tion by sharp­en­ing con­cen­tra­tion, accel­er­at­ing infor­ma­tion pro­cess­ing, and strength­en­ing visu­al mem­o­ry, lead­ing to improved mem­o­ry and sus­tained focus. But as any enthu­si­ast of Japan­ese craft cul­ture knows, no mat­ter how much hard­er it may be to do things with ana­log tools, some­times it’s just more sat­is­fy­ing.

Relat­ed Con­tent:

Free Online Math Cours­es

The Won­der­ful Wood­en Mar­ble Adding Machine

The Math­e­mat­ics Behind Origa­mi, the Ancient Japan­ese Art of Paper Fold­ing

Com­plex Math Made Sim­ple With Engag­ing Ani­ma­tions: Fouri­er Trans­form, Cal­cu­lus, Lin­ear Alge­bra, Neur­al Net­works & More

Japan­ese Musi­cians Turn Obso­lete Machines Into Musi­cal Instru­ments: Cath­ode Ray Tube TVs, Over­head Pro­jec­tors, Reel-to-Reel Tape Machines & More

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. He’s the author of the newslet­ter Books on Cities as well as the books 한국 요약 금지 (No Sum­ma­riz­ing Korea) and Kore­an Newtro. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

The World’s Oldest Homework: A Look at Babylonian Math Homework from 4,000 Years Ago

Home­work has late­ly become unfash­ion­able, at least accord­ing to what I’ve heard from teach­ers in cer­tain parts of the Unit­ed States. That may com­pli­cate var­i­ous fair­ly long-stand­ing edu­ca­tion­al prac­tices, but it does­n’t nec­es­sar­i­ly reflect an absolute drop in stan­dards and expec­ta­tions. Those of us who went to school around the turn of the mil­len­ni­um may remem­ber feel­ing entombed in home­work, an inten­si­fied ver­sion of what the gen­er­a­tion that came of age amid the ear­ly Cold War’s pres­sure for “more sci­ence,” would have dealt with. But late baby boomers and ear­ly Gen-Xers in the six­ties and sev­en­ties had a much lighter load, as did the gen­er­a­tion edu­cat­ed under John Dewey’s reforms of the ear­ly twen­ti­eth cen­tu­ry.

We can fol­low this line all the way back to the times of the Baby­lo­ni­ans, 4,000 years ago. In the video above from her chan­nel Tibees, sci­ence YouTu­ber Toby Hendy shows us a few arti­facts of home­work from antiq­ui­ty and explains how to inter­pret them.

Inscribed in a clay tablet, their sim­ple but numer­ous marks reveal them to be exam­ples of math home­work, that most loathed cat­e­go­ry today, and per­haps then as well. (Even when inter­pret­ed in mod­ern lan­guage, the cal­cu­la­tions may seem unfa­mil­iar, per­formed as they are not in our base ten, but base 60 — shades of the “new math” to come much lat­er.) That the Baby­lo­ni­ans had fair­ly advanced math­e­mat­ics, which Hendy demon­strates using some clay of her own, may be as much of a sur­prise as the fact that they did home­work.

Not that they all did it. Uni­ver­sal school­ing itself dates only from the indus­tri­al age, and for the Baby­lo­ni­ans, indus­try was still a long way off. They did, how­ev­er, take the con­sid­er­able step of cre­at­ing civ­i­liza­tion, which they could­n’t have done with­out writ­ing. The ancient assign­ment Hendy shows would’ve been done by a stu­dent at an edu­ba, which she describes as a “scribe school.” Scribe, as we know, means one who writes — which, in Baby­lon, meant one who writes in Sumer­ian. That skill was trans­mit­ted through the net­work of edu­ba, or “house where tablets are passed out,” which were usu­al­ly locat­ed in pri­vate res­i­dences, and which turned out grad­u­ates lit­er­ate and numer­ate enough to keep the empire run­ning, at least until the sixth cen­tu­ry BC or so. From cer­tain destruc­tive forces, it seems, no amount of home­work can pro­tect a civ­i­liza­tion for­ev­er.

Relat­ed con­tent:

An Ancient Egypt­ian Home­work Assign­ment from 1800 Years Ago: Some Things Are Tru­ly Time­less

A 4,000-Year-Old Stu­dent ‘Writ­ing Board’ from Ancient Egypt (with Teacher’s Cor­rec­tions in Red)

3,200-Year-Old Egypt­ian Tablet Records Excus­es for Why Peo­ple Missed Work: “The Scor­pi­on Bit Him,” “Brew­ing Beer” & More

Archae­ol­o­gists Think They’ve Dis­cov­ered the Old­est Greek Copy of Homer’s Odyssey: 13 Vers­es on a Clay Tablet

Behold the Old­est Writ­ten Text in the World: The Kish Tablet, Cir­ca 3500 BC

Hear the Ear­li­est Record­ed Cus­tomer Com­plaint Let­ter: From Ancient Sume­ria 1750 BC

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

The World Record for the Shortest Math Article: 2 Words

In 2004, John Con­way and Alexan­der Soifer, both work­ing on math­e­mat­ics at Prince­ton Uni­ver­si­ty, sub­mit­ted to the Amer­i­can Math­e­mat­i­cal Month­ly what they believed was “a new world record in the num­ber of words in a [math] paper.”

Soifer explains: “On April 28, 2004 … I sub­mit­ted our paper that includ­ed just two words, ‘n2 + 2 can’ and our two draw­ings. [See one of them above.]” The sto­ry then con­tin­ues: “The Amer­i­can Math­e­mat­i­cal Month­ly was sur­prised, and did not know what to do about our new world record of a 2‑word arti­cle. Two days lat­er, on April 30, 2004, the Edi­to­r­i­al Assis­tant Mrs. Mar­garet Combs acknowl­edged the receipt of the paper”:

The Month­ly pub­lish­es expo­si­tion of math­e­mat­ics at many lev­els, and it con­tains arti­cles both long and short. Your arti­cle, how­ev­er, is a bit too short to be a good Month­ly arti­cle… A line or two of expla­na­tion would real­ly help.

Soifer writ­ers: “The same day at the cof­fee hour I asked John [Con­way], ‘What do you think?’ His answer was con­cise, ‘Do not give up too eas­i­ly.’ Accord­ing­ly, I replied [to] The Month­ly the same day”:

I respect­ful­ly dis­agree that a short paper in general—and this paper in particular—merely due to its size must be “a bit too short to be a good Month­ly arti­cle.” Is there a con­nec­tion between quan­ti­ty and qual­i­ty?… We have posed a fine (in our opin­ion) open prob­lem and report­ed two dis­tinct “behold-style” proofs of our advance on this prob­lem. What else is there to explain?

Soifer adds: “The Month­ly, appar­ent­ly felt out­gunned, for on May 4, 2004, the reply came from The Month­ly’s top gun, Edi­tor-in-Chief Bruce Pal­ka”:

The Month­ly pub­lish­es two types of papers: “arti­cles,” which are sub­stan­tive expos­i­to­ry papers rang­ing in length from about six to twen­ty-five pages, and “notes,” which are short­er, fre­quent­ly some­what more tech­ni­cal pieces (typ­i­cal­ly in the one-to-five page range). I can send your paper to the notes edi­tor if you wish, but I expect that he’ll not be inter­est­ed in it either because of its length and lack of any sub­stan­tial accom­pa­ny­ing text. The stan­dard way in which we use such short papers these days is as “boxed filler” on pages that would oth­er­wise con­tain a lot of the blank space that pub­lish­ers abhor. If you’d allow us to use your paper in that way, I’d be hap­py to pub­lish it.

Soifer con­cludes: “John Con­way and I accept­ed the ‘filler’, and in the Jan­u­ary 2005 issue our paper was pub­lished.” Vic­to­ry!

Get more of the back­sto­ry here.

Relat­ed Con­tent:

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

John Nash’s Super Short PhD The­sis: 26 Pages & Two Cita­tions

The Map of Math­e­mat­ics: Ani­ma­tion Shows How All the Dif­fer­ent Fields in Math Fit Togeth­er

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John Nash’s Super Short PhD Thesis: 26 Pages & Two Citations

When John Nash wrote “Non-Coop­er­a­tive Games,” his Ph.D. dis­ser­ta­tion at Prince­ton in 1950, the text of his the­sis (read it online) was brief. It ran only 26 pages. And more par­tic­u­lar­ly, it was light on cita­tions. Nash’s diss cit­ed two texts: John von Neu­mann and Oskar Mor­gen­stern’s The­o­ry of Games and Eco­nom­ic Behav­ior (1944), which essen­tial­ly cre­at­ed game the­o­ry and rev­o­lu­tion­ized the field of eco­nom­ics; the oth­er cit­ed text, “Equi­lib­ri­um Points in n‑Person Games,” was an arti­cle writ­ten by Nash him­self. And it laid the foun­da­tion for his dis­ser­ta­tion, anoth­er sem­i­nal work in the devel­op­ment of game the­o­ry, for which Nash was award­ed the Nobel Prize in Eco­nom­ic Sci­ences in 1994.

The reward of invent­ing a new field is hav­ing a slim bib­li­og­ra­phy.

If you would like to sup­port the mis­sion of Open Cul­ture, con­sid­er mak­ing a dona­tion to our site. It’s hard to rely 100% on ads, and your con­tri­bu­tions will help us con­tin­ue pro­vid­ing the best free cul­tur­al and edu­ca­tion­al mate­ri­als to learn­ers every­where. You can con­tribute through Pay­Pal, Patre­on, and Ven­mo (@openculture). Thanks!

Note: An ear­li­er ver­sion of this post appeared on our site in June, 2015.

Relat­ed Con­tent:

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

The World Record for the Short­est Math Arti­cle: 2 Words

Doc­tor­al Dis­ser­ta­tion as a Graph­ic Nov­el: Read a Free Excerpt of Nick Sou­sa­nis’ Unflat­ten­ing

How to Dance Your Dis­ser­ta­tion: See the Win­ning Video in the 2014 “Dance Your PhD” Con­test

Umber­to Eco’s How To Write a The­sis: A Wit­ty, Irrev­er­ent & High­ly Prac­ti­cal Guide Now Out in Eng­lish

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The Map of Mathematics: Animation Shows How All the Different Fields in Math Fit Together

Back in Decem­ber, you hope­ful­ly thor­ough­ly immersed your­self in The Map of Physics, an ani­mat­ed video–a visu­al aid for the mod­ern age–that mapped out the field of physics, explain­ing all the con­nec­tions between clas­si­cal physics, quan­tum physics, and rel­a­tiv­i­ty.

You can’t do physics with­out math. Hence we now have The Map of Math­e­mat­ics. Cre­at­ed by physi­cist Dominic Wal­li­man, this video explains “how pure math­e­mat­ics and applied math­e­mat­ics relate to each oth­er and all of the sub-top­ics they are made from.” Watch the new video above. You can buy a poster of the map here. And you can down­load a ver­sion for edu­ca­tion­al use here.

If you would like to sup­port the mis­sion of Open Cul­ture, con­sid­er mak­ing a dona­tion to our site. It’s hard to rely 100% on ads, and your con­tri­bu­tions will help us con­tin­ue pro­vid­ing the best free cul­tur­al and edu­ca­tion­al mate­ri­als to learn­ers every­where. You can con­tribute through Pay­Pal, Patre­on, and Ven­mo (@openculture). Thanks!

Relat­ed Con­tent 

Com­plex Math Made Sim­ple With Engag­ing Ani­ma­tions: Fouri­er Trans­form, Cal­cu­lus, Lin­ear Alge­bra, Neur­al Net­works & More

John Coltrane Draws a Pic­ture Illus­trat­ing the Math­e­mat­ics of Music

The Ele­gant Math­e­mat­ics of Vit­ru­vian Man, Leonar­do da Vinci’s Most Famous Draw­ing: An Ani­mat­ed Intro­duc­tion

The Math Behind Beethoven’s Music

Free Online Math Cours­es

 

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The Decimal Point Is 150 Years Older Than We Thought, Emerging in Renaissance Italy

His­to­ri­ans have long thought that the dec­i­mal point first came into use in 1593, when the Ger­man math­e­mati­cian Christo­pher Clav­ius wrote an astron­o­my text called Astro­labi­um. It turns out, how­ev­er, that the his­to­ry of the dec­i­mal point stretch­es back anoth­er 150 years–to the work of the Venet­ian mer­chant Gio­van­ni Bian­chi­ni. In his text Tab­u­lae pri­mi mobilis, writ­ten dur­ing the 1440s, Bian­chi­ni used the dec­i­mal point to cal­cu­late the coor­di­nates of plan­ets. In so doing, he invent­ed a sys­tem of dec­i­mal frac­tions, which, in turn, made the cal­cu­la­tions under­pin­ning mod­ern sci­ence more effi­cient and less com­plex, notes Sci­en­tif­ic Amer­i­can.

Glen Van Brum­me­len, a his­to­ri­an of math­e­mat­ics, recent­ly recount­ed to NPR how he dis­cov­ered Bian­chini’s inno­va­tion:

I was work­ing on the man­u­script of this astronomer, Gio­van­ni Bian­chi­ni. I saw the dots inside of a table — in a numer­i­cal table. And when he explained his cal­cu­la­tions, it became clear that what he was doing was exact­ly the same thing as we do with the dec­i­mal point. And I’m afraid I got rather excit­ed at that point. I grabbed my com­put­er, ran up and down the dorm hall­way look­ing for col­leagues who still had­n’t gone to bed, say­ing, this per­son­’s work­ing with the dec­i­mal point in the 1440s. I think they prob­a­bly thought I was crazy.

In a new arti­cle appear­ing in the jour­nal His­to­ria Math­e­mat­i­ca, Van Brum­me­len explains the his­tor­i­cal sig­nif­i­cance of the dec­i­mal point, and what this dis­cov­ery means for the his­tor­i­cal devel­op­ment of math­e­mat­ics. You can read it online.

Relat­ed Con­tent 

Trigonom­e­try Dis­cov­ered on a 3700-Year-Old Ancient Baby­lon­ian Tablet

How the Ancient Greeks Shaped Mod­ern Math­e­mat­ics: A Short, Ani­mat­ed Intro­duc­tion

The Map of Math­e­mat­ics: An Ani­mat­ed Video Shows How All the Dif­fer­ent Fields in Math Fit Togeth­er

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