Edmund Orme Harriss (born 1976 in Worcester, UK) is a British mathematician,Experiencing Mathematics – Edmund Harriss at Imperial College London
11 December 2018 writer and artist. Since 2010 he has been at the Fulbright College of Arts & Sciences at The

University of Arkansas The University of Arkansas (U of A, UArk, or UA) is a Public university, public Land-grant university, land-grant research university in Fayetteville, Arkansas, United States. It is the Flagship campus, flagship campus of the University of Arkan ...

Fayetteville, Arkansas Fayetteville ( ) is the List of cities and towns in Arkansas, second-most populous city in the U.S. state of Arkansas, the county seat of Washington County, Arkansas, Washington County, and the most populous city in Northwest Arkansas. The city ...

where he is an Assistant Professor of Arts & Sciences (ARSC) and Mathematical Sciences (MASC). He does research in the Geometry of

Tilings and Patterns ''Tilings and patterns'' is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed. Structu ...

, a branch of

Convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

and

Discrete Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory * Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit * Discrete group, ...

Geometry.Edmund Orme Harriss
at ResearchGate He is the discoverer of the spiral that bears his name.The golden ratio has spawned a beautiful new curve: the Harriss spiral
The Guardian, 13 January 2015

Education and career

Harriss earned a

Master of Mathematics A Master of Mathematics (or MMath) degree is a specific advanced integrated Master's degree for courses in the field of mathematics. United Kingdom In the United Kingdom, the MMath is the internationally recognized standard qualification after a f ...

at the

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands and Warwickshire, England. The university was founded in 1965 as part of ...

(2000) and then obtained his PhD at

Imperial College London Imperial College London, also known as Imperial, is a Public university, public research university in London, England. Its history began with Prince Albert of Saxe-Coburg and Gotha, Prince Albert, husband of Queen Victoria, who envisioned a Al ...

(2003) with the dissertation "On Canonical Substitution Tilings" under Jeroen Lamb. Harriss has been a speaker at

FSCONS Free Society Conference and Nordic Summit (FSCONS) is a Nordic conference trying to bridge the gap between software and cultural freedom held each autumn in Gothenburg, Sweden. It shares many similarities with FOSDEM (Free and Open source Software ...

, a Nordic Free software conference. Harriss is active on

Numberphile ''Numberphile'' is an Educational entertainment, educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, but the channe ...

where he has given talks on Heesch numbers,

Tribonacci number In mathematics, the Fibonacci numbers form a sequence defined recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci seq ...

s, the

Rauzy fractal In mathematics, the Rauzy fractal is a fractal set associated with the Tribonacci substitution : s(1)=12,\ s(2)=13,\ s(3)=1 \,. It was studied in 1981 by Gérard Rauzy, with the idea of generalizing the dynamic properties of the Fibonacci mor ...

and the

plastic ratio In mathematics, the plastic ratio is a geometrical aspect ratio, proportion, given by the unique real polynomial root, solution of the equation Its decimal expansion begins as . The adjective ''plastic'' does not refer to Plastic, the artifici ...

. In May and June 2020 Harriss was a visiting fellow at The Institute for Advanced Study of

Aix-Marseille University Aix-Marseille University (AMU; ; formally incorporated as ) is a Public university, public research university located in the Provence region of southern France. It was founded in 1409 when Louis II of Anjou, List of rulers of Provence, Count of ...

(IMéRA) where he studied the possibilities of visual and spatial models and animations to illustrate a wide variety of mathematical ideas.

Mathematical art

The

Gauss–Bonnet theorem In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a Surface (topology), surface to its underlying topology. In the simplest applicati ...

gives the relationship between the curvature of a surface and the amount of turning as you traverse the surface’s boundary. Harriss used this theorem to invent shapes called Curvahedra which were then incorporated into sculpture. Scientists at MIT are investigating ways in which curvahedra may have applications in construction. Art and mathematics are intertwined in Harris's work.Edmund Harriss bio
Aix-Marseille University He uses public art to demonstrate deep mathematical ideasHonors College, Gearharts Dedicate Curvahedra Sculpture
University of Arkansas NEWS, Oct. 21, 2021 and his academic work frequently involves the visualization of mathematics. Mathematically themed sculptures by Harriss have been installed at

Oklahoma State University Oklahoma State University (informally Oklahoma State or OSU) is a public land-grant research university in Stillwater, Oklahoma, United States. The university was established in 1890 under the legislation of the Morrill Act. Originally known ...

, at the University of Arkansas,Courtyard Curvahedra
By Kendall Curlee, University of Arkansas: A+ Online 2021 and at

. Combining his interest in art and mathematical tilings he is one of 24 mathematicians and artists who make up the Mathemalchemy Team.Art Installation Celebrates the Beauty and Whimsy of Math
Duke Today, November 9, 2021

Harriss Spiral

Harriss noticed that the

golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \fr ...

is just one example of a more general idea: In how many ways can a rectangle be divided into squares and rectangles? The golden ratio results when a rectangle is divided into a one square and one similar rectangle. But by varying the number of squares and sub-rectangles, we arrive at what Harriss calls "proportion systems". The solutions in all cases are algebraic numbers and the golden ratio is just one of them. : "The golden ratio is this incredibly well-explored corner of a whole city,” he said. “I wanted to give signposts to other locations in that city." Harriss investigated the next simplest case, dividing a rectangle into one square and ''two'' similar rectangles. The ratio that emerged in this case is the so-called

.On the cover: Harriss spiral
by Matthew Scroggs and Edmund Harriss, Chalkdust Magazine, 14 March 2019 The

golden spiral In geometry, a golden spiral is a logarithmic spiral whose growth factor is , the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of for every quarter Turn (angle), turn it makes. Approximations of th ...

is closely related to the first case, dissection into one square and one similar rectangle. Harriss applied the same idea to this second case and discovered a new

fractal In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scale ...

spiral In mathematics, a spiral is a curve which emanates from a point, moving further away as it revolves around the point. It is a subtype of whorled patterns, a broad group that also includes concentric objects. Two-dimensional A two-dimension ...

related to the

and since named after him.

Selected publications

Books

Harriss has published several books designed to spread joy in mathematics. The sales of his colouring books run well beyond 100,000.Colouring-in books boom continues with volume of mathematical patterns
, by Alison Flood,

The Guardian ''The Guardian'' is a British daily newspaper. It was founded in Manchester in 1821 as ''The Manchester Guardian'' and changed its name in 1959, followed by a move to London. Along with its sister paper, ''The Guardian Weekly'', ''The Guardi ...

, 06 Jul 2015 * (2015) ''Snowflake Seashell Star: Colouring Adventures in Numberland '' with Alex Bellos * (2016) ''Patterns of the Universe: A Coloring Adventure in Math and Beauty'', with Alex Bellos Patterns of the Universe A Coloring Adventure in Math and Beauty
,

Science Magazine ''Science'' is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscrib ...

, 01 Jan 2016, Vol 351, Issue 6268, p. 36 * (2016) ''Visions of the Universe: A Coloring Journey Through Math's Great Mysteries'', with Alex Bellos * (2020) ''Hello Numbers! What Can You Do? 'An Adventure Beyond Counting'', with Houston Hughes, Illustrated by Brian Rea

Papers

* (2011
"From oranges to modems" in "The unplanned impact of mathematics"
Nature, vol 475, pp. 166–169 * (2011)
Algebraic numbers, free group automorphisms and substitutions on the plane
with Pierre Arnoux, Maki Furukado and Shunji Ito,

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of pure and applied mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must ...

363 (2011), pp. 4651-4699 * (2015)
Strain and the optoelectronic properties of nonplanar phosphorene monolayers
with Mehrshad Mehboudi et al, Proceedings of the National Academy of Sciences of the United States of America * (2020)
Algebraic Number Starscapes
with Katherine E. Stange and Steve Trettel

References

External links

Edmund O. Harriss website
{{DEFAULTSORT:Harriss, Edmund University of Arkansas faculty Alumni of the University of Warwick Alumni of Imperial College London 21st-century English mathematicians Recreational mathematicians Mathematics popularizers 1976 births Living people Mathematical artists 21st-century British sculptors 21st-century English male writers Writers from Worcester, England English male sculptors 21st-century English male artists