Oliver Byrne: The Matisse of Mathematics - Byrne's Euclid: Geometry Understood via Color-coded Diagrams

Oliver Byrne’s most celebrated work, 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, was published in London by William Pickering in 1847. Byrne claimed to have conducted experiments showing that Euclid’s Elements could be mastered using this color method “in less than one third of the time usually employed.”⁹⁶ His expressed aim was “to teach people how to think and not what to think.”⁹⁷ In his final Royal Literary Fund application in 1880, Byrne wrote,⁹⁸

These works … have a greater aim than mere illustration; 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.

Figure 11. Title page of Oliver Byrne's 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 from the copy owned by Sid Kolpas. Note the royal stamp in the upper right corner reading "Sample: Department Of Science and Art." This stamp may indicate that this copy of Byrne's book was exhibited in London during the Great Exhibition of 1851.

Byrne’s 1847 Euclid was one of the first multicolor printed books, and is today the most renowned and valuable of his works. Many consider it the most attractive edition of Euclid’s Elements ever produced. Byrne's Euclid was extremely difficult and expensive to produce, requiring exact registration of the pages in order to print each color, the typeface, and the vignettes; therefore, only one thousand copies were originally published. According to retired University College Dublin meteorology professor and mathematics blogger, Peter Lynch, the book was regarded as a curiosity, and was largely ignored; it did not sell well at a price of 25 shillings, almost five times the typical book price at the time.⁹⁹

Historian of art and architecture Werner Oechslin, in his preface to the beautiful facsimile, Oliver Byrne: The Elements of Euclid (see Figure 11, below), wrote that¹⁰⁰

no one who holds it in his hands can resist the fascination of its illustrations. The pictures are more captivating because they simply suggest, concretely demonstrate ad oculus and thus assist in the comprehension of mathematical laws that initially seem most difficult and abstract.

Figure 12. Facsimile of Oliver Byrne's 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, edited by Werner Oechslin and published as Oliver Byrne: The Elements of Euclid by Taschen in 2013. (Image of the copy owned by Sid Kolpas)

Byrne, according to Peter Lynch, “was not in the vanguard of mathematical thought.”¹⁰¹ In Byrne's time, Euclid's Elements was the geometry text used in British schools, but there was considerable debate about its suitability. Mathematicians such as Charles Dodgson (1832-1898), who wrote children's literature as Lewis Carroll, in his book Euclid and His Modern Rivals (1879), and Augustus De Morgan (1806-1871) debated how appropriate it was to teach Euclid's classical version of geometry versus a more modern approach.¹⁰² Byrne felt, as does Sid Kolpas, that geometry is the basis of all of mathematical science, and should provide a student's first formal experience with proof, the bedrock of mathematical thought.

Written and designed purportedly to simplify Euclid’s geometry, Byrne's Euclid was an extraordinary example of Victorian printing and was described by typographer and book designer Ruari McLean in Victorian Book Design and Colour Printing as “one of the oddest and most beautiful books of the whole century.”¹⁰³ McLean described each page as

a unique riot of red, yellow and blue: on some pages letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers, demanding the most meticulous register; elsewhere, solid squares, triangles, and circles are printed in gaudy and theatrical colors, attaining a verve not seen again on book pages till the days of Dufy, Matisse and Derain.

McLean labeled Byrne’s work “… a decided complication of Euclid.” Often, a pedagogical prophet is not recognized by his or her peers.

Figure 13. This page from Oliver Byrne's Elements of Euclid displays “a unique riot of red, yellow, and blue, reminiscent of Matisse,” in the words of modern typographer and book designer Ruari McLean. (Image from the book in the collection of Sid Kolpas)

Historian of mathematics and mathematics educator Florian Cajori (1859-1930) had a mixed opinion of the pedagogical approach of Byrne's Euclid. After asserting that the use of colored diagrams and symbols was “a noteworthy device for aiding the young mind through sensuous stimulus,” he speculated that “the failure of the book is doubtless due to the want of moderation in the use of colors.”¹⁰⁴ David Eugene Smith (1860-1944), another historian of mathematics and mathematics educator, was also guarded in his opinion of Byrne's approach, stating that “[t]here is some merit in speaking of the red triangle instead of the triangle ABC, but not enough to give the method any standing.”¹⁰⁵ It is Sid Kolpas' opinion, in agreement with Cajori and Smith, that Byrne's magnum opus is not well suited as a stand-alone geometry text, but is best used as a supplement to a geometry course, along with labeled diagrams, traditional proof, and algebraic argument; that way, it is not "a decided complication of Euclid," but rather an aid to better understanding Euclid's arguments. Mathematician Bill Casselman believes that while Byrne's Euclid's “failures are interesting, … for students it has proved to be a fruitful source of projects.”¹⁰⁶ In fact, Kolpas has successfully used Byrne's work as a source of student projects, and as an inspiration for using color-coded diagrams within a traditional teaching approach.

Contrary to McLean, Cajori, and Smith, Edward R. Tufte, pioneer in the visualization of data, indicated in his Envisioning Information that Byrne’s design may greatly clarify Euclid’s Elements for students with a visual preference for learning.¹⁰⁷ That is, Byrne created a book that would help right-brained students master the complexities of geometry! Modern pedagogy teaches us that it is best to appeal to the visual, auditory, and kinesthetic senses when teaching mathematics. In the preface to his Euclid, Byrne stated that the traditional oral and written demonstrations of Euclid are enhanced by color dissections. To quote Byrne’s preface:¹⁰⁸

Sounds which address the ear are lost and die
In one short hour, but these which strike the eye,
Live long upon the mind, the faithful sight
Engraves the knowledge with a beam of light.

Byrne further indicated in his preface that he subscribed to the pedagogy of the Swiss educator Johann Heinrich Pestalozzi (1746-1827), considered by many to be the Father of Modern Education. Pestalozzi felt that education should be interactive and should appeal to all of the senses; the use of colored dissections enhances that appeal. It should be noted that Byrne’s Euclid was not his only attempt at using color and strongly visual explanations of mathematical concepts, similar to “proofs without words.” In his The Young Geometrician, published in 1865, Byrne set out to teach geometric constructions with the use of color. Moreover, according to Ruari McLean in a letter to the second author, Byrne also intended to create a calculus text with the use of color dissections.¹⁰⁹ The book was proofed, but never printed. Byrne indicated in the proof copy that the calculus text would be “uniform with The Coloured Euclid.”

Figure 14. Page from Oliver Byrne's The Young Geometrician. (Image from the book in the collection of Sid Kolpas)

Byrne’s 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 was designed and printed by the acclaimed printer Charles Whittingham (1795-1876) of the Chiswick Press. The book's use of color was its most striking feature, with equal angles, lines, or polygonal regions assigned the same bright primary color, and its colored shapes surely must have presented the greatest challenge to the printer. However, its more traditional black print was intricate and beautiful, too. Each proposition was set in black Caslon italic, with a beautifully engraved four-line initial vignette, usually an “I” for “If” or “In” (see Figure 15). A four-line initial vignette therefore begins most pages in Byrne’s Euclid. Caslon is a group of beautiful serif typefaces designed by William Caslon (1692–1766). According to the Society of Printers, “It was at the Chiswick Press that the use of the old-face Caslon type was revived in 1843. . . [A] revival followed by printers throughout England.”¹¹⁰ At least three women assisted Whittingham: his daughters Charlotte and Elizabeth Whittingham studied art and calligraphy, and Mary Byfield turned their designs into beautiful wood engravings and made other contributions to the business as well. According to the Dictionary of National Biography,¹¹¹

Charlotte and Elizabeth were educated as artists, and from their designs came the greater part of the extensive collection of borders, monograms, head and tail pieces, and other embellishments still preserved and used. The engraver of most of the ornamental wood-blocks was Mary Byfield (d. 1871).

Byrne’s Euclid benefited from their beautiful work.

Figure 15. The "initials" above were used to begin first sentences of sections in Byrne's Euclid. (These images are provided courtesy of William A. Casselman, Department of Mathematics, University of British Columbia, and appear at his website www.math.ubc.ca. They were made from a copy of Byrne's 1847 Euclid held by the Thomas L. Fisher Rare Book Library, University of Toronto.)

According to Julie L. Mellby, graphic arts librarian at Princeton University, in her online article "Euclid in Color," Byrne's Euclid was exhibited in London at the Great Exhibition of 1851.¹¹² Praise was given for its beauty and the artistry of the printing, which may have influenced future publications and artwork. However, the book was sold for an extravagant price by contemporary standards, placing it out of the reach of educators who were supposed to make use of this new way of teaching geometry. Given the royal stamp on the upper right hand corner of the title page indicating "Sample: Department Of Science And Art," the second author suspects that his copy of Byrne's Euclid might have been a sample copy at the Great Exhibition.

Today, due to its rarity and beauty, Byrne’s 1847 Euclid is an extremely valuable book, sold for an extravagant price by modern standards. At the time of this writing, if one could find a copy similar in condition to the one in the second author's rare book collection, it might cost as much as $22,500. Fortunately, one can purchase the beautiful full color facsimile shown in Figure 12, above, edited by art and architecture historian Werner Oechslin and published by Taschen America. Moreover, Bill Casselman has made available an image of each page of Byrne’s Euclid at the University of British Columbia’s web site: www.math.ubc.ca/~cass/Euclid/byrne.html. Teachers can make use of these images in their lessons.

Ideas for using Byrne’s Euclid in the mathematics classroom can be found on the next two pages.

96 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 (London: William Pickering, 1847), ix.

97 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 (London: William Pickering, 1847), xvii.

98 RLF application (28 June 1880).

99 Peter Lynch, “That’s Maths: The rebel who brought Technicolour to Euclid,” Irish Times, February 20, 2014.

100 Werner Oechslin, ed., Oliver Byrne: The Elements of Euclid (Cologne, Germany: Taschen America LLC, 2013), 15.

101 Peter Lynch, “That’s Maths: The rebel who brought Technicolour to Euclid,” Irish Times, February 20, 2014.

102 Lewis Carroll (Charles Dodgson), Euclid and his Modern Rivals (New York: Dover Publications, 1973; originally published in 1879).

103 Ruari McLean, Victorian Book Design and Colour Printing (London: Faber and Faber, 1963), 50-51.

104 Florian Cajori, “Attempts Made During the Eighteenth and Nineteenth Centuries to Reform the Teaching of Geometry,” The American Mathematical Monthly, 17:10 (1910), 194. The opinions held by various historians about Byrne's Euclid are summarized in Janet Heine Barnett's article, “Mathematics is a Plural Noun: The Case of Oliver Byrne,” Proceedings of the Canadian Society for the History and Philosophy of Mathematics: Thirty-fifth Annual Meeting (Montreal), 23:26-46 (2010).

105 Smith, David Eugene, ed., Augustus De Morgan, and Sophia Elizabeth De Morgan, A Budget of Paradoxes, by Augustus de Morgan, 2nd ed. (Chicago and London: The Open Court Publishing Company, 1915; originally published in 1872), Volume I, p. 329.

106 Bill Casselman, “Pictures and Proofs,” AMS Notices, 47:10 (2000), 1257-1266.

107 Edward R. Tufte, Envisioning Information (Cheshire, Connecticut: Graph Press, 1990).

108 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 (London: William Pickering, 1847), xii.

109 Ruari McLean to Dr. Sid Kolpas, letter, June 29, 1993.

110 Society of Printers, The Development of Printing as an Art: A Handbook of the Exhibition in Honor of the Bi-Centenary of Franklin's Birth Held at the Boston Public Library under the auspices of the Society of Printers (Society of Printers: Boston, Massachusetts, 1906), 26.

111 Sidney Lee, ed., Dictionary of National Biography, 1885-1900 (London: Smith, Elder & Co., 1900), 61:148.

112 Mellby, Julie L., "Euclid in Color," Princeton University Library, Princeton, New Jersey, 2008. https://blogs.princeton.edu/graphicarts/2008/05/euclid_in_color.html