(figure 1)

Quote from Dr David Stewart, Lecturer in Pure Mathematics, Newcastle University:

"It is impossible to imagine mathematics as it is now without Euclid’s Elements. The Elements was by far the most successful textbook of all time, not least because it set down so magnificently the principle that all mathematics can be built up rigorously from basic notions. At least one very important idea in algebra we use all the time is that of a Euclidean domain. This is a type of algebraic structure which has a division with remainders technique familiar from Euclid’s book—Euclid uses this technique for whole numbers and so we call it Euclid’s algorithm. Euclidean domains have lots of important useful properties like unique factorisation. Understanding how far an algebraic structure is from having unique factorisation brings one to calculating the ideal class group and from that into class field theory and beyond, right into very modern algebraic number theory."

To find out about current research in Pure Mathematics (including geometry) at Newcastle University, please explore the following link: http://www.ncl.ac.uk/maths-physics/research/pure/

Reference (figure 1): Artmann, B. (2016) 'Euclidean geometry’, in Encyclopedia Britannica. (2018). Available at: https://www.britannica.com/science/Euclidean-geometry (Accessed 16/03/2018).

Architecture begins with geometry, it lies at the core of the architectural design process and is apparent from the initial stages of design to the actual construction.  Since earliest times, builders relied on imitating natural forms, then applied mathematical principles to standardize and replicate the forms. Roman architect, Marcus Vitruvius, was the first to document the proportions for how structures should be constructed and wrote down some rules about architecture in his famous Ten Books on Architecture (De Architectura). Vitruvius believed that builders should always use precise ratios when constructing and famously quoted "without symmetry and proportion no temple can have a regular plan". In contemporary architecture there are no fixed rules about design concepts, but there are still associations to geometric space concepts - modern constructive geometry provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes apparent in architecture today.

The publications available, via the link on this page, showcase some of the work carried out in the School of Architecture, Planning and Design http://www.ncl.ac.uk/apl/gallery/publications/

References

Craven, J (2017) Architecture, geometry, and the Vitruvian Man: Where do we see geometry in architecture? Available at https://www.thoughtco.com/geometry-and-architecture-178081 (Accessed: 26/03/18).

Leopold, C (2006). Geometry concepts in architectural design. Available at https://www.researchgate.net/publication/237544451_GEOMETRY_CONCEPTS_IN_ARCHITECTURAL_DESIGN (Accessed 26/03/18).

Pottmann, H et al (2007). Architectural geometry. Exton: Bentley Institute Press.

Of all the disciplines in engineering, civil engineering uses geometry the most. Geometry involves surveying the earth and the analysis and study of relationships between shapes; civil engineers design and assemble shapes to construct buildings, bridges, roads, tunnels, dams etc. and use geometry to find the strongest angles to build supports to make these structures as strong as possible. Ancient Greek principals taught centuries ago are still used today to create structurally sound constructions, although computers are used to carry out a lot of the geometric analysis, a strong conceptual knowledge of how geometry works is still a requirement for civil engineers.

To find out about current research in Civil Engineering at Newcastle University, please explore the following link: http://www.ncl.ac.uk/engineering/research/civil/

References

IAC Publishing (2018). How is geometry used in engineering? Available at https://www.reference.com/math/geometry-used-engineering-61cda8c8758634f6 (Accessed 29/03/18).

IEEE (2018). What is the application of geometry to civil engineering? Available at http://tryengineering.org/ask-expert/what-application-geometry-civil-engineering (Accessed 26/03/18).

Strucalc (2017). Structural engineering and geometry. Available at http://www.strucalc.com/structural-engineering-and-geometry/ (Accessed 26/03/18).

                                    Sean Scully: 1970, Newcastle Bridge 1972

Geometry offers the most obvious connection between mathematics and art, the two disciplines involve drawing and the use of shapes and forms, as well as an understanding of spatial concepts, two and three dimensions, measurement, estimation, and pattern. Leonardo Da Vinci’s Mona Lisa, is drawn according to the golden ratio. Some art movements that use geometric shapes include Bauhaus, Cubism, Futurism and Vorticism, many sculptors also use geometric shapes in their work.

Sean Scully is one of the leading artists of his generation, he studied art at Newcastle University from 1968 until 1972, Sean has developed and refined his own recognisable style of geometric abstraction, creating large works using horizontal and vertical stripes, bands and grids in numerous configurations, more information about Sean can be found at the following link http://www.ncl.ac.uk/press/articles/latest/2018/01/seanscully/

References

City of Los Angeles Department of Cultural Affairs (2011).  LAMCA Evenings for Educators: Geometry and art, symmetry, balance, scale Available at: http://www.lacma.org/eduprograms/EvesforEds/GeoEssay.pdf (Accessed: 26/03/18).

Glydon, N (no date). The mathematics of art. Available at mathcentral.uregina.ca/beyond/articles/art/art1.html  (Accessed: 26/03/18).