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Reimagining Byrne’s Euclid

Cover of Euclid's Elements of Geometry, by Kronecker Wallis

Barcelona-based publishing company Kronecker Wallis have produced a new updated edition of Byrne’s Euclid. We asked founder and editor Jordi Anton to tell us all about it – and their related Principia reprint, which is still looking for funding on Kickstarter.

Tell us about Euclid’s Elements.

Euclid of Alexandria lived c. 300 BCE. He wrote The Elements, the most widely used mathematics and geometry textbook in history. The Elements consists of thirteen books. In all, it contains 465 theorems and proofs, described in a clear, logical and elegant style, and using only a compass and a straight edge. Euclid’s Elements has influenced all branches of science but none so much as mathematics and the exact sciences. No other book except the Bible has been so widely translated and circulated.  

The first printed version of the Elements appeared in 1482 with the advent of the printing press. It was based on Campanus of Novara’s 1260 edition. On May 25, 1482 printer Erhard Ratdolt of Venice issued the first printed edition of Euclid’s Elements. It was the first substantial book to contain geometrical figures. From definitions and axioms, Euclid showed how to prove dozens of mathematical propositions, producing knowledge that was objective and undeniable.

Isaac Newton’s famous work Principia Mathematica clearly demonstrates Euclid’s influence. Newton called his famous laws of motion “axioms” and deduced his law of gravitation in the form of two mathematical theorems.

Page 12 from Book 1 of Byrne's Euclid
Page 12 from Book 1 of Oliver Byrne’s edition of The Elements

Who was Oliver Byrne, and what did he do?

Irish-born Oliver Byrne (1810-1880) was an innovator in mathematics education, particularly in the teaching of geometry. His most well-known book was his colorful version of ‘Euclid’s Elements’, published in 1847. Oliver Byrne employed a red, yellow, and blue color scheme for the figures and diagrams in his most unusual 1847 edition of Euclid’s Elements.

“I do not introduce colours for the purpose of entertainment, or to amuse by certain combinations of tint and form, but to assist the mind in its researches after truth, to increase the facilities of instruction, and to diffuse permanent knowledge”.

 Oliver Byrne

Byrne had experimented with colors in schools and he had evidently decided that the schoolteacher’s approach indicating lines, angles,… on the blackboard and then making deductions from them would be better described by his method than in the usual way.

Oliver Byrne’s 1847 Euclid was one of the first multicolor printed books. Many consider it the most attractive edition of Euclid’s Elements ever produced.Byrne’s Euclid was exhibited in London at the Great Exhibition of 1851. Praise was given for its beauty and the artistry of the printing, which may have influenced future publications and artwork.

You might have noticed we’re fans of Byrne’s diagrams here at the Aperiodical (see: our header images and branding). What drew you to Byrne’s work?

After printing Isaac Newton’s Principia, we were searching for another major book in science. We have been in love with Elements for a long time and as design enthusiasts, Byrne’s work held a special place in our minds. Those beautiful, minimalist, clean and didactical lines encouraged us to start a crazy adventure, to finish Byrne’s work. All 13 books.
It simply could not be unfinished!

A page from Kronecker Wallis' edition of The Elements

What’s different between your edition and Byrne’s original?

The first six books are identical. We only applied a modern vectorial design to graphs and a new typography, but the content is the same. Our hard work started when creating the visual interpretation of the rest of the books, from 7 to 13.

Who took on the challenge of reinterpreting Euclid’s work on books 7-13?

A team of 6 mathematicians worked almost a year and a half – thinking, drawing and writing every page of the books. The team not only have great mathematical skills, but also a deep knowledge of mathematics history and mathematics didactic.

Were there any challenges presented by content in the later books?

Absolutely. Almost all the later books were a challenge, especially the 10th. This book involved a very long journey for our mathematicians. Not only talking about maths – the entire project was a challenge because we needed to manage a large team of mathematicians, designers, editors… taking our small company nearly to its limits – it was hard and difficult to adapt a lot of non-geometrical propositions; lots of points-of-view, a lot of nights thinking how to solve a problem… but in the end we have achieved what we believe to be an outstanding end result. 

How did you incorporate Byrne’s unique graphical style for the less visual content?

We were faithful to Byrne’s philosophy and before any designer started to work, we created a visual guide for internal use. With that guide, we worked together with mathematicians re-using graphical elements and creating some new ones – because books 7 – 13 needed a new color (some graphs needed more than Byrne’s three basic colors).But focusing on your question, for the less visual content, we followed Byrne’s color scheme and put it into the text as imaginary words.

A page from Kronecker Wallis' edition of The Elements

What’s the target audience for your book? Why should we buy an expensive paper edition when free, interactive versions are available online?

We are intrinsically ‘digital’ and know that physical books nowadays can seem hard to manage and expensive….thats the reason we print books with high quality papers and with a love for design. We try to keep an eye on the details and quality. We have a high respect for our customers and want to create books that meet their expectations (when they are committed to not relying on the free digital versions) – it’s our priority. Obviously, our Elements is an expensive book because it was very expensive to produce. Much more than our other books.

We smiled when we found out that Byrne’s Euclid was extremely difficult and expensive to produce. Only one thousand copies (almost like our crowdfunding campaign) were originally published. It was sold at a price of 25 shillings, almost five times the typical book price at the time. Maybe we are also close to that ‘five times the amount’ with our book – compared to a typical book.

Our audience are science lovers. A lot of our customers send us ideas of new books, authors,… and they are science people. But also they love well-produced books and buy them as collectors because our books are books to own, not only to read. We do not know how to, nor do we want to, create a monotonous and characterless product. We want to create books to own and create the desire to touch unique books made by lovers of books and science. Not only for customers.

What have you learned from this project?

Patience! We published it with a few delays because we prioritized quality and good content versus speed. That meant, people had to have a lot of patience with us waiting for their books without asking. We love our customers and supporters, they are the most important motivation for us.
Also, we learned how beautiful mathematics can be and the power of joining mathematics and design – to reach more people and understand math better.

Poster version of the cover of book 12 of Kronecker Wallis' edition of The Elements

As well as the book itself, are there any related products people can pick up? (I’m thinking posters. I want a poster.)

Yes! Posters – we created a poster of every book cover. The cover design is our creation, Byrne didn’t create them. They are truly beautiful.

At the other hand, our Newton’s Principia could be also a related product. Newton used Euclid’s Elements knowledge and language to introduce his theorems. Since last Tuesday we are trying to reprint it again.

What’s your next project? Is it also maths-related?

Now we are only focused on a 6-book Astronomy collection. We did a Kickstarter campaign earlier this year, and we are working hard now on translations. Another challenge for us!

We don’t know which will be our next big project. I’ll keep you posted!

TeXnique: a LaTeX typesetting game

You know what’s fun? Typesetting mathematics! Glad you agree, because here’s a game that puts the fun in ‘underfilled hbox’.

Screenshot of TeXnique. A box showing the target formula above a box showing a rendering of code typed in the box below.

In TeXnique, you’re shown a typeset bit of mathematical notation, and have to frantically type LaTeX to reproduce it. You get three minutes, and you’re awarded points when you produce something that’s a pixel-perfect replica of the original. Think Typing of the Dead crossed with The Art of Computer Programming.

When I first saw this I rolled my eyes, but now my high score is 68 and I don’t know why I keep going back to it.

The formulas are largely well-known snippets of notation, so you might find some of them coming out through muscle memory, but if a symbol shows up that you can’t remember the macro for, there’s always the brilliant Detexify tool.

Play: by Akshay Ravikumar.

Carnival of Maths 172

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of July, is now online at Cassandra Lee Yieng’s blog.

Carnival of Maths 172

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

Maths at the Edinburgh Fringe, 2019

As the hordes descend upon the city of Edinburgh for another August-ful of comedy, theatre, arts and culture, the question I’m sure you’re asking yourself is, ‘what about the maths?’ Zero problem: we’re here with a quick guide to some of the big pluses you’ll find in the Fringe Guide.

Alan Turing is the face of the new £50 note

The Bank of England has announced, following a public poll, that the new £50 note will feature mathematician, cryptographer and computer science pioneer Alan Turing. While this might seem like unambiguous good news, the issues it raises are more complicated than they first appear. Here’s a guest post from LGBT+ mathematician Calvin Smith with his thoughts on the decision.

Image result for £50 note

It’s obviously fabulous that Alan Turing is being recognised on the new £50 note, but this joy at seeing a gay mathematician given this recognition is tainted with the memory of his cruel treatment by the society of the day and the ongoing persecution of queer and trans people today.

It’s absolutely right that we celebrate the achievements of Turing the mathematician, and I’m hoping that this also creates an opportunity to talk more about the amazing work he did away from his well-known code-breaking in the field of mathematical biology, where he developed models which help us to understand the formation of shapes and patterns in biology. As a gay man working in mathematics I’m also hoping that the additional prominence given to Turing’s work acts as a further catalyst to drive inclusion in STEM subjects and that more young queer people consider study and careers in these areas.

If we are committed to doing the best science and solving modern problems then we need the most diverse set of thinkers available and for each of them to be able to bring their whole authentic selves to work. There are some wonderful organisations like Pride In Stem and events like the LGBT STEMinar which bring together and give voice to a diverse mix of queer scientists who can otherwise feel invisible or over-exposed in their local work environment. Stonewall’s work in making workplaces (especially universities) more LGBT+ inclusive cannot be underestimated as a driver for positive change. Hopefully the greater awareness and visibility afforded by Turing can drive improvements: the future of science is fabulously queer and intersectional. Fire the glitter cannon!

However, setting aside my maths-joy at seeing another mathematician celebrated I’m also filled with a cocktail of bitterness and seething rage at this announcement. Turing and society’s treatment of him is hugely symbolic and cannot be underestimated. Turing’s appearance on a bank note does not excuse society its historic treatment of him of other victims of homophobia. Just because we now have same-sex marriage does not mean the fight for queer inclusion is over. I grew up under Section 28 telling me that homosexual relationships were “pretend families” and while I am now a proud gay dad to two lovely scamps it is worth reflecting that Section 28 was only repealed in 2003, same-sex adoption introduced in 2005. Many of our recent victories seem fragile and culturally we still have a long way to go to eradicate the homophobia, lesbophobia, biphobia and transphobia which continues to lead to assaults on queer people to this day. Turing is also a call to action and constant vigilance so that we don’t turn the clock back on acceptance without exception, on inclusion for all, and for no outsiders.

July is LGBT wrath month: a Turing banknote cannot be allowed to become a pinkwashed sticking plaster over the underlying issues of intolerance, and we need LGBT+ people and their allies to continue the fight so that it remains a call to action – and not the undeserved pat on the back which leads to complacency and the further loss of queer and trans lives.

Carnival of Mathematics 171

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of June, is now online at MathTuition88.

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.