This Is What an 1869 MIT Entrance Exam Looks Like: Could You Have Passed the Test?

in Education, Math, MIT | May 27th, 2020

The late 19th Cen­tu­ry was the time of Charles Dar­win and James Clerk Maxwell, of Thomas Edi­son and Alexan­der Gra­ham Bell. It was a gold­en age of sci­ence and tech­nol­o­gy. So you might won­der how hard it was to get into one of the top tech­ni­cal uni­ver­si­ties in that era.

The answer, accord­ing to this video? Not very hard.

At least that was the case in 1869 at the Mass­a­chu­setts Insti­tute of Tech­nol­o­gy, or MIT,  as the young Aus­tralian sci­ence and math teacher Toby Hendy explains on her excel­lent YouTube chan­nel, Tibees. MIT was brand new and des­per­ate for tuition rev­enue in 1869, so the object of the test was­n’t to whit­tle a mas­sive field of appli­cants down to a man­age­able size. It was sim­ply to make sure that incom­ing stu­dents could han­dle the work.

MIT opened in 1865, just after the end of the Civ­il War. The idea was to cre­ate a Euro­pean-style poly­tech­nic uni­ver­si­ty to meet the demands of an increas­ing­ly indus­tri­al econ­o­my. The orig­i­nal cam­pus was in Boston, across the Charles Riv­er from its cur­rent loca­tion in Cam­bridge. Only 15 stu­dents signed up in 1865. Tuition was $100 for the whole year. There was no for­mal entrance test. Accord­ing to an arti­cle from the school’s Archives and Spe­cial Col­lec­tions,

The “con­di­tions for admis­sion” sec­tion of MIT’s cat­a­logue for 1865–66 indi­cates that can­di­dates for admis­sion as first year stu­dents must be at least six­teen years old and must give sat­is­fac­to­ry evi­dence “by exam­i­na­tion or oth­er­wise” of a com­pe­tent train­ing in arith­metic, geom­e­try, Eng­lish gram­mar, geog­ra­phy, and the “rudi­ments of French.” Rapid and leg­i­ble hand­writ­ing was also stressed as being “par­tic­u­lar­ly impor­tant.” By 1869 the hand­writ­ing require­ment and French had been dropped, but alge­bra had been added and stu­dents need­ed to pass a qual­i­fy­ing exam in the required sub­ject areas. An ancil­lary effect was to pro­tect unqual­i­fied stu­dents from dis­ap­point­ment and pro­fes­sors from wast­ing their time.

A cou­ple of years ear­li­er, in 1867, the MIT Exec­u­tive Com­mit­tee report­ed that fac­ul­ty mem­bers had felt it nec­es­sary to ask par­ents of “some incom­pe­tent and inat­ten­tive stu­dents to with­draw them from the school, wish­ing to spare them the mor­ti­fi­ca­tion of an exam­i­na­tion which it was cer­tain they could not pass.”

Nowa­days, the stu­dents who make it into MIT have aver­age SAT and ACT scores in the 99th per­centile. Of 21,312 first-year appli­cants hop­ing to join the Class of 2023, only 1,427 made it. That’s an admis­sion rate of 6.7 per­cent. What a dif­fer­ence 150 years can make!

To take the 1869 entrance exam­i­na­tion in Eng­lish, Alge­bra, Geom­e­try and Arith­metic, and to see the cor­rect answers, vis­it this cached arti­cle from the MIT web­site.

Relat­ed Con­tent:

Free Online Math Cours­es

Albert Ein­stein’s Grades: A Fas­ci­nat­ing Look at His Report Cards

Teacher Calls Jacques Der­ri­da’s Col­lege Admis­sion Essay on Shake­speare “Quite Incom­pre­hen­si­ble” (1951)

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

in Math | February 27th, 2020

shortest math paper

Euler’s con­jec­ture, a the­o­ry pro­posed by Leon­hard Euler in 1769, hung in there for 200 years. Then L.J. Lan­der and T.R. Parkin came along in 1966, and debunked the con­jec­ture in two swift sen­tences. Their arti­cle — which is now open access and can be down­loaded here — appeared in the Bul­letin of the Amer­i­can Math­e­mat­i­cal Soci­ety. If you’re won­der­ing what the con­jec­ture and its refu­ta­tion are all about, you might want to ask Cliff Pick­over, the author of 45 books on math and sci­ence. He brought this curi­ous doc­u­ment to the web back in 2015.

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:

60 Free Online Math Cours­es

Free Math Text­books

The Math in Good Will Hunt­ing is Easy: How Do You Like Them Apples?

Does Math Objec­tive­ly Exist, or Is It a Human Cre­ation? A New PBS Video Explores a Time­less Ques­tion

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Discover Kōlams, the Traditional Indian Patterns That Combine Art, Mathematics & Magic

in Art, Math, Religion | May 20th, 2019

Have accom­plished abstract geo­met­ri­cal artists come out of any demo­graph­ic in greater num­bers than from the women of South Asia? Not when even the most demand­ing art-school cur­ricu­lum can’t hope to equal the rig­or of the kōlam, a com­plex kind of line draw­ing prac­ticed by women every­where from India to Sri Lan­ka to Malaysia to Thai­land. Using hum­ble mate­ri­als like chalk and rice flour on the ground in front of their homes, they inter­weave not just lines, shapes, and pat­terns but reli­gious, philo­soph­i­cal, and mag­i­cal motifs as well — and they cre­ate their kōlams anew each and every day.

“Feed­ing A Thou­sand Souls: Kōlam” by Thacher Gallery at the Uni­ver­si­ty of San Fran­cis­co is licensed under CC BY-SA 2.0

“Tak­ing a clump of rice flour in a bowl (or a coconut shell), the kōlam artist steps onto her fresh­ly washed can­vas: the ground at the entrance of her house, or any patch of floor mark­ing an entry­point,” writes Atlas Obscu­ra’s Rohi­ni Cha­ki.

“Work­ing swift­ly, she takes pinch­es of rice flour and draws geo­met­ric pat­terns: curved lines, labyrinthine loops around red or white dots, hexag­o­nal frac­tals, or flo­ral pat­terns resem­bling the lotus, a sym­bol of the god­dess of pros­per­i­ty, Lak­sh­mi, for whom the kōlam is drawn as a prayer in illus­tra­tion.”

Col­or­ful Kolam — Sivasankaran — Own work

Kōlams are thought to bring pros­per­i­ty, but they also have oth­er uses, such as feed­ing ants, birds, and oth­er pass­ing crea­tures. Cha­ki quotes Uni­ver­si­ty of San Fran­cis­co The­ol­o­gy and Reli­gious Stud­ies pro­fes­sor Vijaya Nagara­jan as describ­ing their ful­fill­ing the Hin­du “karmic oblig­a­tion” to “feed a thou­sand souls.” Kōlams have also become an object of gen­uine inter­est for math­e­mati­cians and com­put­er sci­en­tists due to their recur­sive nature: “They start out small, but can be built out by con­tin­u­ing to enlarge the same sub­pat­tern, cre­at­ing a com­plex over­all design,” Cha­ki writes. “This has fas­ci­nat­ed math­e­mati­cians, because the pat­terns elu­ci­date fun­da­men­tal math­e­mat­i­cal prin­ci­ples.”

“Kolam” by resakse is licensed under CC BY-ND 2.0

Like any tra­di­tion­al art form, the kōlam does­n’t have quite as many prac­ti­tion­ers as it used to, much less prac­ti­tion­ers who can meet the stan­dard of mas­tery of com­plet­ing an entire work with­out once stand­ing up or even lift­ing their hand. But even so, the kōlam is hard­ly on the brink of dying out: you can see a few of their cre­ators in action in the video at the top of the post, and the age of social media has offered kōlam cre­ators of any age — and now even the occa­sion­al man — the kind of expo­sure that even the busiest front door could nev­er match. Some who get into kōlams in the 21st cen­tu­ry may want to cre­ate ones that show ever more com­plex­i­ty of geom­e­try and depth of ref­er­ence, but the best among them won’t for­get the mean­ing, accord­ing to Cha­ki, of the for­m’s very name: beau­ty.

Read more about kōlams at Atlas Obscu­ra.

Relat­ed Con­tent:

Math­e­mat­ics Made Vis­i­ble: The Extra­or­di­nary Math­e­mat­i­cal Art of M.C. Esch­er

New Iran­ian Video Game, Engare, Explores the Ele­gant Geom­e­try of Islam­ic Art

The Com­plex Geom­e­try of Islam­ic Art & Design: A Short Intro­duc­tion

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les and the video series The City in Cin­e­ma. Fol­low him on Twit­ter at @colinmarshall, on Face­book, or on Insta­gram.

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Why the World’s Best Mathematicians Are Hoarding Japanese Chalk

in Math | May 7th, 2019

Here’s the lat­est from Great Big Sto­ry: “Once upon a time, not long ago, the math world fell in love … with a chalk. But not just any chalk! This was Hagoro­mo: a Japan­ese brand so smooth, so per­fect that some won­dered if it was made from the tears of angels. Pen­cils down, please, as we tell the tale of a writ­ing imple­ment so irre­place­able, pro­fes­sors stock­piled it.”

Head over to Ama­zon and try to buy it, and all you get is: “Cur­rent­ly unavail­able. We don’t know when or if this item will be back in stock.” Indeed, they’ve stock­piled it all.

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:

Stephen Hawking’s Lec­tures on Black Holes Now Ful­ly Ani­mat­ed with Chalk­board Illus­tra­tions

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

Free Online Math Cours­es

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Pioneering Computer Scientist Grace Hopper Shows Us How to Visualize a Nanosecond (1983)

in Computer Science, Math, Physics | May 7th, 2019

Human imag­i­na­tion seems seri­ous­ly lim­it­ed when faced with the cos­mic scope of time and space. We can imag­ine, through stop-motion ani­ma­tion and CGI, what it might be like to walk the earth with crea­tures the size of office build­ings. But how to wrap our heads around the fact that they lived hun­dreds of mil­lions of years ago, on a plan­et some four and a half bil­lion years old? We trust the sci­ence, but can’t rely on intu­ition alone to guide us to such mind-bog­gling knowl­edge.

At the oth­er end of the scale, events mea­sured in nanosec­onds, or bil­lionths of a sec­ond, seem incon­ceiv­able, even to some­one as smart as Grace Hop­per, the Navy math­e­mati­cian who invent­ed COBOL and helped built the first com­put­er. Or so she says in the 1983 video clip above from one of her many lec­tures in her role as a guest lec­tur­er at uni­ver­si­ties, muse­ums, mil­i­tary bod­ies, and cor­po­ra­tions.

When she first heard of “cir­cuits that act­ed in nanosec­onds,” she says, “bil­lionths of a sec­ond… Well, I didn’t know what a bil­lion was…. And if you don’t know what a bil­lion is, how on earth do you know what a bil­lionth is? Final­ly, one morn­ing in total des­per­a­tion, I called over the engi­neer­ing build­ing, and I said, ‘Please cut off a nanosec­ond and send it to me.” What she asked for, she explains, and shows the class, was a piece of wire rep­re­sent­ing the dis­tance a sig­nal could trav­el in a nanosec­ond.

Now of course it wouldn’t real­ly be through wire — it’d be out in space, the veloc­i­ty of light. So if we start with a veloc­i­ty of light and use your friend­ly com­put­er, you’ll dis­cov­er that a nanosec­ond is 11.8 inch­es long, the max­i­mum lim­it­ing dis­tance that elec­tric­i­ty can trav­el in a bil­lionth of a sec­ond.

Fol­low the rest of her expla­na­tion, with wire props, and see if you can bet­ter under­stand a mea­sure of time beyond the reach­es of con­scious expe­ri­ence. The expla­na­tion was imme­di­ate­ly suc­cess­ful when she began using it in the late 1960s “to demon­strate how design­ing small­er com­po­nents would pro­duce faster com­put­ers,” writes the Nation­al Muse­um of Amer­i­can His­to­ry. The bun­dle of wires below, each about 30cm (11.8 inch­es) long, comes from a lec­ture Hop­per gave muse­um docents in March 1985.

Pho­to via the Nation­al Muse­um of Amer­i­can His­to­ry

Like the age of the dinosaurs, the nanosec­ond may only rep­re­sent a small frac­tion of the incom­pre­hen­si­bly small units of time sci­en­tists are even­tu­al­ly able to measure—and com­put­er sci­en­tists able to access. “Lat­er,” notes the NMAH, “as com­po­nents shrank and com­put­er speeds increased, Hop­per used grains of pep­per to rep­re­sent the dis­tance elec­tric­i­ty trav­eled in a picosec­ond, one tril­lionth of a sec­ond.”

At this point, the map becomes no more reveal­ing than the unknown ter­ri­to­ry, invis­i­ble to the naked eye, incon­ceiv­able but through wild leaps of imag­i­na­tion. But if any­one could explain the increas­ing­ly inex­plic­a­ble in terms most any­one could under­stand, it was the bril­liant but down-to-earth Hop­per.

via Kot­tke

Relat­ed Con­tent:

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

The Map of Com­put­er Sci­ence: New Ani­ma­tion Presents a Sur­vey of Com­put­er Sci­ence, from Alan Tur­ing to “Aug­ment­ed Real­i­ty”

Free Online Com­put­er Sci­ence Cours­es 

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness

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How Leonardo da Vinci Drew an Accurate Satellite Map of an Italian City (1502)

in Art, History, Maps, Math | April 16th, 2019

When I look at maps from cen­turies ago, I won­der how they could have been of any use. Not only were they filled with mytho­log­i­cal mon­sters and mytho­log­i­cal places, but the per­spec­tives most­ly served an aes­thet­ic design rather than a prac­ti­cal one. Of course, accu­ra­cy was hard to come by with­out the many map­ping tools we take for granted—some of them just in their infan­cy dur­ing the Renais­sance, and many more that would have seemed like out­landish mag­ic to near­ly every­one in 15th cen­tu­ry Europe.

Every­one, it some­times seems, but Leonar­do da Vin­ci, who antic­i­pat­ed and some­times steered the direc­tion of futur­is­tic pub­lic works tech­nol­o­gy. None of his fly­ing machines worked, and he could hard­ly have seen images tak­en from out­er space. But he clear­ly saw the prob­lem with con­tem­po­rary maps. The neces­si­ty of fix­ing them led to a 1502 aer­i­al image of Imo­la, Italy, drawn almost as accu­rate­ly as if he had been peer­ing at the city through a Google satel­lite cam­era.

“Leonar­do,” says the nar­ra­tor of the Vox video above, “need­ed to show Imo­la as an ichno­graph­ic map,” a term coined by ancient Roman engi­neer Vit­ru­vius to describe ground plan-style car­tog­ra­phy. No streets or build­ings are obscured, as they are in the maps drawn from the oblique per­spec­tive of a hill­top or moun­tain. Leonar­do under­took the project while employed as Cesare Borgia’s mil­i­tary engi­neer. “He was charged with help­ing Bor­gia become more aware of the town’s lay­out.” For this visu­al aid turned car­to­graph­ic mar­vel, he drew from the same source that inspired the ele­gant Vit­ru­vian Man.

While the vision­ary Roman builder could imag­ine a god’s eye view, it took some­one with Leonardo’s extra­or­di­nary per­spi­cac­i­ty and skill to actu­al­ly draw one, in a star­tling­ly accu­rate way. Did he do it with grit and mox­ie? Did he astral project thou­sands of miles above the city? Was he in con­tact with ancient aliens? No, he used geom­e­try, and a com­pass, the same means and instru­ments that allowed ancient sci­en­tists like Eratos­thenes to cal­cu­late the cir­cum­fer­ence of the earth, to with­in 200 miles, over 2000 years ago.

Leonar­do prob­a­bly also used an instru­ment called a bus­so­la, a device that mea­sures degrees inside a circle—like the one that sur­rounds his city map. Painstak­ing­ly record­ing the angles of each turn and inter­sec­tion in the town and mea­sur­ing their dis­tance from each oth­er would have giv­en him the data he need­ed to recre­ate the city as seen from above, using the bus­so­la to main­tain prop­er scale. Oth­er meth­ods would have been involved, all of them com­mon­ly avail­able to sur­vey­ors, builders, city plan­ners, and car­tog­ra­phers at the time. Leonar­do trust­ed the math, even though he could nev­er ver­i­fy it, but like the best map­mak­ers, he also want­ed to make some­thing beau­ti­ful.

It may be dif­fi­cult for his­to­ri­ans to deter­mine which inac­cu­ra­cies are due to mis­cal­cu­la­tion and which to delib­er­ate dis­tor­tion for some artis­tic pur­pose. But license or mis­takes aside, Leonardo’s map remains an aston­ish­ing feat, mark­ing a seis­mic shift from the geog­ra­phy of “myth and per­cep­tion” to one of “infor­ma­tion, drawn plain­ly.” There’s no telling if the arche­typ­al Renais­sance man would have liked where this path led, but if he lived in the 21st cen­tu­ry, he’d already have his mind trained on ideas that antic­i­pate tech­nol­o­gy hun­dreds of years in our future.

Relat­ed Con­tent:

Carl Sagan Explains How the Ancient Greeks, Using Rea­son and Math, Fig­ured Out the Earth Isn’t Flat, Over 2,000 Years Ago

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

Leonar­do da Vin­ci Saw the World Dif­fer­ent­ly… Thanks to an Eye Dis­or­der, Says a New Sci­en­tif­ic Study

Leonar­do da Vinci’s Ear­li­est Note­books Now Dig­i­tized and Made Free Online: Explore His Inge­nious Draw­ings, Dia­grams, Mir­ror Writ­ing & More

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness

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

in Animation, Math | January 15th, 2019

In many an audio engi­neer­ing course, I’ve come across the Fouri­er Trans­form, an idea so fun­da­men­tal in sound pro­duc­tion that it seems essen­tial for every­one to know it. My lim­it­ed under­stand­ing was, you might say, func­tion­al. It’s some kind of math­e­mat­i­cal reverse engi­neer­ing machine that turns wave­forms into fre­quen­cies, right? Yes, but it’s much more than that. The idea can seem over­whelm­ing to the non-math­e­mat­i­cal­ly-inclined among us.

The Fouri­er Trans­form, named for French math­e­mati­cian and physi­cist Jean-Bap­tiste Joseph Fouri­er, “decom­pos­es” any wave form into fre­quen­cies, and “vir­tu­al­ly every­thing in the world can be described via a wave­form,” writes one intro­duc­tion to the the­o­ry. That includes not only sounds but “elec­tro­mag­net­ic fields, the ele­va­tion of a hill ver­sus loca­tion… the price of  your favorite stock ver­sus time,” the sig­nals of an MRI scan­ner.

The con­cept “extends well beyond sound and fre­quen­cy into many dis­parate areas of math and even physics. It is crazy just how ubiq­ui­tous this idea is,” notes the 3Blue1Brown video above, one of dozens of ani­mat­ed explo­rations of math­e­mat­i­cal con­cepts. I know far more than I did yes­ter­day thanks to this com­pre­hen­sive ani­mat­ed lec­ture. Even if it all seems old hat to you, “there is some­thing fun and enrich­ing,” the video assures us, “about see­ing what all of its com­po­nents look like.”

Things get com­pli­cat­ed rather quick­ly when we get into the dense equa­tions, but the video illus­trates every for­mu­la with graphs that trans­form the num­bers into mean­ing­ful mov­ing images.

3Blue1Brown, a project of for­mer Khan Acad­e­my fel­low Grant Sander­son, has done the same for dozens of STEM con­cepts, includ­ing such sub­jects as high­er dimen­sions, cryp­tocur­ren­cies, machine learn­ing, and neur­al net­works and essen­tials of cal­cu­lus and lin­ear alge­bra like the deriv­a­tive para­dox and “Vec­tors, what even are they?”

In short­er lessons, you can learn to count to 1000 on two hands, or, just below, learn what it feels like to invent math. (It feels weird at first.)

Sander­son­’s short cours­es “tend to fall into one of two cat­e­gories,” he writes: top­ics “peo­ple might be seek­ing out,” like many of those men­tioned above, and “prob­lems in math which many peo­ple may not have heard of, and which seem real­ly hard at first, but where some shift in per­spec­tive makes it both doable and beau­ti­ful.” These puz­zles with ele­gant­ly clever solu­tions can be found here. Whether you’re a hard­core math-head or not, you’ll find Sanderson’s series of 3Blue1Brown ani­ma­tions illu­mi­nat­ing. Find them all here.

Relat­ed Con­tent:

Free Online Math Cours­es

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

Cit­i­zen Maths: A Free Online Course That Teach­es Adults the Math They Missed in High School

Free Math Text­books 

Math Mag­ic

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness

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A Beautifully-Designed Edition of Euclid’s Elements from 1847 Gets Digitized: Explore the New Online, Interactive Reproduction

in Art, Books, Math | December 19th, 2018

For two mil­len­nia, Euclid­’s Ele­ments, the foun­da­tion­al ancient work on geom­e­try by the famed Greek math­e­mati­cian, was required read­ing for edu­cat­ed peo­ple. (The “clas­si­cal­ly edu­cat­ed” read them in the orig­i­nal Greek.) The influ­ence of the Ele­ments in phi­los­o­phy and math­e­mat­ics can­not be over­stat­ed; so inspir­ing are Euclid’s proofs and axioms that Edna St. Vin­cent Mil­lay wrote a son­net in his hon­or. But over time, Euclid’s prin­ci­ples were stream­lined into text­books, and the Ele­ments was read less and less.

In 1847, maybe sens­ing that the pop­u­lar­i­ty of Euclid’s text was fad­ing, Irish pro­fes­sor of math­e­mat­ics Oliv­er Byrne worked with Lon­don pub­lish­er William Pick­er­ing to pro­duce his own edi­tion of the Ele­ments, or half of it, with orig­i­nal illus­tra­tions that care­ful­ly explain the text.

“Byrne’s edi­tion was one of the first mul­ti­col­or print­ed books,” writes design­er Nicholas Rougeux. “The pre­cise use of col­ors and dia­grams meant that the book was very chal­leng­ing and expen­sive to repro­duce.” It met with lit­tle notice at the time.

Byrne’s edi­tion—The First Six Books of The Ele­ments of Euclid in which Coloured Dia­grams and Sym­bols are Used Instead of Let­ters for the Greater Ease of Learn­ers—might have passed into obscu­ri­ty had a ref­er­ence to it in Edward Tufte’s Envi­sion­ing Infor­ma­tion not sparked renewed inter­est. From there fol­lowed a beau­ti­ful new edi­tion by TASCHEN and an arti­cle on Byrne’s dia­grams in math­e­mat­ics jour­nal Con­ver­gence. Rougeux picked up the thread and decid­ed to cre­ate an online ver­sion. “Like oth­ers,” he writes, “I was drawn to its beau­ti­ful dia­grams and typog­ra­phy.” He has done both of those fea­tures ample jus­tice.

As in anoth­er of Rougeux’s online reproductions—his Werner’s Nomen­cla­ture of Colours—the design­er has tak­en a great deal of care to pre­serve the orig­i­nal inten­tions while adapt­ing the book to the web. In this case, that means the spelling (includ­ing the use of the long s), type­face (Caslon), styl­ized ini­tial cap­i­tals, and Byrne’s alter­nate designs for math­e­mat­i­cal sym­bols have all been retained. But Rougeux has also made the dia­grams inter­ac­tive, “with click­able shapes to aid in under­stand­ing the shapes being ref­er­enced.”

He has also turned all of those love­ly dia­grams into an attrac­tive poster you can hang on the wall for quick ref­er­ence or as a con­ver­sa­tion piece, though this sem­a­phore-like arrange­ment of illustrations—like the sim­pli­fied Euclid in mod­ern textbooks—cannot replace or sup­plant the orig­i­nal text. You can read Euclid in ancient Greek (see a primer here), in Latin and Ara­bic, in Eng­lish trans­la­tions here, here, here, and many oth­er places and lan­guages as well.

For an expe­ri­ence that com­bines, how­ev­er, the best of ancient wis­dom and mod­ern infor­ma­tion technology—from both the 19th and the 21st cen­turies—Rougeux’s free, online edi­tion of Byrne’s Euclid can’t be beat. Learn more about the metic­u­lous process of recre­at­ing Byrne’s text and dia­grams (illus­trat­ed above) here.

Relat­ed Con­tent:

Explore an Inter­ac­tive, Online Ver­sion of Werner’s Nomen­cla­ture of Colours, a 200-Year-Old Guide to the Col­ors of the Nat­ur­al World

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

Where to Find Free Text­books

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness

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