https://sandromagri.info/en/math123/sgp/index.html… It seems to me, in addition to this, to discern in Sarsi a firm belief, that in philosophizing it is necessary to lean on the opinions of some celebrated author, so that our mind, when it is not wedded to the discourse of another, should in everything remain sterile and fruitless; and perhaps estimates that philosophy is a book and a man’s fantasy, like the Iliad and ‘Orlando furioso, books in which the least important thing is that what is written in them is true. Mr. Sarsi, the thing is not like that. Philosophy is written in this very great book that continually stands open before our eyes (I say the universe), but it cannot be understood unless we first learn to understand the language, and know the characters, in which it is written. He is written in the mathematical language, and the characters are triangles, circles, and other geometrical figures, without which means it is impossible to humanly understand a word of it; without these it is a vain wandering through a dark labyrinth. Galileo Galilei (The Assayer, ch. VI, 1623)Hugoensandro@freenetst.it (Sandro Magrì)sandro@freenetst.it (Sandro Magrì)2020- All rights reserved.Fri, 05 Jan 2024 14:21:28 +0100https://sandromagri.info/en/math123/sgp/sgp0005/index.htmlTue, 27 Dec 2022 16:46:16 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/sgp/sgp0005/index.htmlWhat is Geometry? Space Generic set whose elements are called points Topology General and abstract definition of concepts such as vicinity, continuity, connection, compactness and convergence, and of the properties of forms that do not change by continuous deformations of space, i.e., without cuts, tears, overlaps and gluing Topological space_ Space with a topology Metrics Definition of distance between points in space, from which we derive the definition of lengths and angles Measure Definition of the magnitude of a subset of points in space, from which derive the definition of area, volume, and so on Metric space_ Topological space_ in which a metric, that is, a distance between two points in space, is defined, and possibly a measure Group of transformations Set of operations acting on the points of the space, with properties such as: 1. existence of inverse, 2. existence of identity or neutral element, 3. group membership of the combination of two transformations, 4. indifference of the order of evaluation of three transformations (associativity). Symmetry Property of the space, or objects contained in it, that remains unchanged after the application of a transformation of a given group GEOMETRY Study of the invariant properties of a metric space with respect to a group of transformations, or symmetries, that preserve the metric Also called Topology is the branch of mathematics that studies topological spaces, the most important basic of mathematics along with Abstract Algebra and the unifying language provided by Category Theory (functors, morphisms, structures, classes and sets.) The term comes from the Greek topos, “place,” and logos, “study.” Topology is the most general discipline underlying Geometry.https://sandromagri.info/en/math123/sgp/sgp0120/index.htmlFri, 05 Jan 2024 14:21:28 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/sgp/sgp0120/index.htmlMathematics in general (and therefore also geometry) John Stillwell - Mathematics and Its History - (3rd ed. 2010) Saunders Mac Lane - Mathematics Form and Function - (1986) Timothy Gowers - The Princeton Companion to Mathematics - (2008) Nicholas J. Hingham - The Princeton Companion to Applied Mathematics - (2015) Richard Earl, James Nicholson - The Concise Oxford Dictionary of Mathematics - (6th ed. 2021) of a more popular nature: Timothy Gowers - Mathematics. A Very Short Introduction transl.it. Mathematics. An introduction. (2004) Alain Goriely - Applied Mathematics. a Very Short Introduction Richard Elwes - Maths 1001: Absolutely Everything That Matters About Mathematics in 1001 Bite-Sized Explanations (2017) Georg Glaeser - A Mathematical Picture Book transl.it. Images of Mathematics Morris Kline - Mathematics in Western Culture - (1964) transl.it. History of an infinite love. Mathematics in Western culture (2023) John Courant, Herbert Rollins, Ian Stewart - What Is Mathematics?: An Elementary Approach to Ideas and Methods - (1944, 2nd ed. 1996) transl. it. What is mathematics? (2000) Mathematics and the real world Apoorva Khare - Beautiful, Simple, Exact, Crazy: Mathematics in the Real World Evan M. Glaezer, John W. McConnell - Real Life Math Saul Stahl, Paul E. Johnson - Mathematics Old and New (2017) Morris Kline - Mathematics for the Nonmathematician Georg Glaeser - Math tools. 500 applications in science and arts (2017) Georg Glaeser - Nature and Numbers: A Mathematical Photo Shooting Ian Stewart - What’s the Use? - (2022) transl.it. What is mathematics for? The unreasonable effectiveness of a discipline (2022) Geometry in general Maciej Dunajski - Geometry. A Very Short Introduction - (2022) Irving Adler - A New Look at Geometry Saul Stahl - Geometry from Euclid to Knots H. Graham Flegg - From Geometry to Topology Georg Glaeser - Geometry and Its Applications in Arts, Nature and Technology (2020) Georg Glaeser, Franz Gruber - Experiencing Geometry, Physics, and Biology (2024) John Barnes - Gems of Geometry John Stillwell - The Four Pillars of Geometry David A. Brannan, Matthew F. Esplen, Jeremy Gray - Geometry David Hilbert, S.Cohn-Vossen - Geometry and the imagination transl.it. Intuitive Geometry Eli Maor, Eugen Jost - Beautiful Geometry transl.it. The art of geometry (2020) Informal topology Richard Earl - Topology: A Very Short Introduction H. Graham Flegg - From Geometry to Topology David S. Richeson - Euler’s Gem: The Polyhedron Formula and the Birth of Topology Robert Messer, Philip Straffin - Topology Now (2006) V.V. Prasolov - Intuitive Topology Sue E. Goodman - Beginning Topology Peter Saveliev - Topology Illustrated (2016) Geometry and Algebra L.Christine Kinsey, Teresa E. Moore - Symmetry, Shape and Space. An Introduction to Mathematics through Geometry D.L. Herrmann, P.J. Sally Jr. - Number, Shape, & Symmetry. An Introduction to Number Theory, Geometry, and Group Theory Seth Braver - The Dark Art of Linear Algebra: An intuitive geometric approach Tim Chartier - When Life is Linear: From Computer Graphics to Bracketology-MAA (2015) Ivan Savov - No Bullshit Guide to Linear Algebra Gerald Farin, Dianne Hansford - Practical Linear Algebra.A Geometry Toolbox Mikhail Postnikov - Lectures on Geometry. semester I-II Symmetry and group theory Kristopher Tapp - Symmetry A Mathematical Exploration John Stillwell - Naive Lie Theory Nathan Carter - Visual Group Theory (2009) David W. Farmer - Groups and symmetry A guide to discovering mathematics Graphs between computer science,discrete geometry and topology Gary Chartrand - Introductory Graph Theory Nora Hartsfield, Gerhard Ringel - Pearls in Graph Theory: A Comprehensive Introduction Maarten van Steen - Graph Theory and Complex Networks. An Introduction (2010). Sergey Dorogovtsev - Lectures on Complex Networks (2010) Node Theory Colin Adams - The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots David W. Farmer, Theodore B. Stanford - Knots and surfaces Alexei Sossinsky, Giselle Weiss - Knots: Mathematics with a Twist Differential geometry Jeffrey R. Weeks - The Shape of Space 3ed (2019) Tristan Needham - Visual Differential Geometry and Forms: : A Mathematical Drama in Five Acts (2021) Boris A. Dubrovin, Sergei P. Novikov, Anatolij T. Fomenko - Contemporary Geometry. Methods and Applications (Vol. 1-3) Richard L. Bishop, Samuel I. Goldberg - Tensor Analysis on Manifolds Geometry and Physics Hermann Weyl - Space Time Matter (1952) Roger Penrose - The Road to Reality. A Complete Guide to the Laws of the Universe (2007) Trad.it. The Road to Reality Pietro G. Frè - A Conceptual History of Space and Symmetry. From Plato to the Superworld - (2019) George F. R. Ellis - Flat and Curved Space-Times (2001) V. I. Arnold - Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians (2014) V. I. Arnold - Experimental Mathematics (2015) V.I. Arnold - Mathematical methods of classical mechanics James Nearing - Mathematical Tools for Physics (2010) Alec J. Schramm - Mathematical Methods and Physical Insights (2022) Frederick W. Bryon, Robert W. Fuller - Mathematics of Classical and Quantum Physics Peter Szekeres - A Course in Modern Mathematical Physics. Groups, Hilbert Space and Differential Geometry (2004) Mikio Nakahara - Geometry, Topology and Physics - 2_ed (2003) Yvonne Choquet-Bruhat - Introduction to General Relativity, Black Holes and Cosmology - (2015) Tudor D. Stanescu - Introduction to Topological Quantum Matter & Quantum Computation - (2020) Popular readings in Italian Jordan Ellenberg - Shape: The hidden geometry in data, society, politics, information, the universe and many other places Piergiorgio Odifreddi - There is room for everyone. The great tale of geometry (2011) Piergiorgio Odifreddi - An escape route. The great tale of modern geometry (2011) Piergiorgio Odifreddi - Abbasso Euclid! The great tale of contemporary geometry (2013) Peter M. Higgins - The mathematics of social networks. introduction to graph theory Edwin Abbott - Flatland. multi-dimensional fantasy story Marco Andreatta - The shape of things. The alphabet of geometry Laura Catastini, Franco Ghione - Geometries without limits: Non-Euclidean worlds Popular readings on symmetry Alan Holden - Shapes, Spaces and Symmetry John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss - The Symmetries of Things Ian Stewart - Symmetry A Very Short Introduction Ian Stewart - Why Beauty Is Truth. The History of Symmetry transl.it. The Elegance of Truth. history of symmetry Ian Stewart, Martin Golubitsky - Fearful Symmetry: Is God a Geometer? transl. it. terrible symmetries. is God a geometer? (1995) Marcus Du Sautoy - Finding Moonshine: A Mathematician’s Journey Through Symmetry - (2012) transl.it. The perfect disorder: A mathematician’s adventure into the secrets of symmetry