Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compass and straightedge, to draw conclusions and solve problems. Only after the introduction of coordinate methods was there a reason to introduce the term "synthetic geometry" to distinguish this approach to geometry from other approaches.Other approaches to geometry are embodied in analytic and algebraic geometries, where one would use analysis and algebraic techniques to obtain geometric results. According to Felix Klein Synthetic geometry is that which studies figures as such, without recourse to formulae, whereas analytic geometry consistently makes use of such formulae as can be written down after the adoption of an appropriate system of coordinates. Geometry as presented by Euclid in the Elements is the quintessential example of the use of the synthetic method. It was the favoured method of Isaac Newton for the solution of geometric problems. Synthetic methods were most prominent during the 19th century when geometers rejected coordinate methods in establishing the foundations of projective geometry and non-Euclidean geometries. For example the geometer Jakob Steiner (1796 – 1863) hated analytic geometry, and always gave preference to synthetic methods. (Wikipedia).
Introduction to Projective Geometry (Part 1)
The first video in a series on projective geometry. We discuss the motivation for studying projective planes, and list the axioms of affine planes.
From playlist Introduction to Projective Geometry
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: Dynamic Interactives!
Classical curves | Differential Geometry 1 | NJ Wildberger
The first lecture of a beginner's course on Differential Geometry! Given by Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications
From playlist Differential Geometry
Surface with Square Cross Sections
Surface with square cross sections and modifiable base: https://www.geogebra.org/m/mcfmabak #GeoGebra #math #geometry #calculus #AugmentedReality
From playlist Calculus: Dynamic Interactives!
Messing with Mona: Introduction to Geometric Transformations
Link: https://www.geogebra.org/m/KFtdRvyv
From playlist Geometry: Dynamic Interactives!
Area of a Regular Polygon: 2 Conceptual Approaches
Links: https://www.geogebra.org/m/aHvgEm9v https://www.geogebra.org/m/wxJFqM9P
From playlist Geometry: Dynamic Interactives!
Create a Triangle with Given Area: Quick Formative Assessment with GeoGebra
GeoGebra Resource: https://www.geogebra.org/m/gbcbbx29
From playlist Geometry: Dynamic Interactives!
Geometric and algebraic aspects of space curves | Differential Geometry 20 | NJ Wildberger
A space curve has associated to it various interesting lines and planes at each point on it. The tangent vector determines a line, normal to that is the normal plane, while the span of adjacent normals (or equivalently the velocity and acceleration) is the osculating plane. In this lectur
From playlist Differential Geometry
Similar Figures Definition: Dynamic Illustration
Link: https://www.geogebra.org/m/EeXdSpJB
From playlist Geometry: Dynamic Interactives!
Symplectic geometry of surface group representations - William Goldman
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Symplectic geometry of surface group representations Speaker: William Goldman Affiliation: Member, School of Mathematics Date: February 28, 2022 If G is a Lie group whose adjoint representation preserves a nondegenerate sy
From playlist Mathematics
GPDE Workshop - Synthetic formulations - Cedric Villani
Cedric Villani IAS/ENS-France February 23, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Flexibility in C^0 symplectic geometry - Lev Buhovsky
Workshop on the h-principle and beyond Topic: Flexibility in C^0 symplectic geometry Speaker: Lev Buhovsky Affiliation: Tel Aviv University Date: November 4, 2021 Abstract: Traditionally, objects of study in symplectic geometry are smooth - such as symplectic and Hamiltonian diffeomorph
From playlist Mathematics
Contact non-squeezing via selective symplectic homology - Igor Uljarević
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Contact non-squeezing via selective symplectic homology Speaker: Igor Uljarević Affiliation: University of Belgrade Date: October 14, 2022 I will introduce a new version of symplectic homology that resembles
From playlist Mathematics
Live CEOing Ep 194: Geometry in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Geometry in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
In search of quantum geometry by Pranav Pandit
COLLOQUIUM IN SEARCH OF QUANTUM GEOMETRY SPEAKER: Pranav Pandit (ICTS - TIFR, Bengaluru) DATE: Mon, 29 November 2021, 15:30 to 17:00 VENUE: Online and Ramanujan Lecture Hall RESOURCES ABSTRACT Notions of geometry have evolved throughout the history of mathematics, often in parallel
From playlist ICTS Colloquia
Fake It Till You Make It (Microsoft) | Paper Explained
❤️ Become The AI Epiphany Patreon ❤️ ► https://www.patreon.com/theaiepiphany 👨👩👧👦 JOIN OUR DISCORD COMMUNITY: Discord ► https://discord.gg/peBrCpheKE 📢 SUBSCRIBE TO MY MONTHLY AI NEWSLETTER: Substack ► https://aiepiphany.substack.com/ In this video I cover Microsoft's "Fake it till
From playlist Computer Vision
algebraic geometry 15 Projective space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry
From playlist Algebraic geometry I: Varieties
SYNTHETIC DIVISION – Algebra 2 /College Algebra/Pre-Calculus
TabletClass Math: https://tcmathacademy.com/ Algebra 2 help with synthetic division and the remainder theorem. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebr
From playlist GED Prep Videos
11_6_1 Contours and Tangents to Contours Part 1
A contour is simply the intersection of the curve of a function and a plane or hyperplane at a specific level. The gradient of the original function is a vector perpendicular to the tangent of the contour at a point on the contour.
From playlist Advanced Calculus / Multivariable Calculus
Construction of Particular Planar Curves using GeoGebra - Florida GeoGebra Conference 2022: Part 13
Here, Petra Surynková leading us in our final Florida GeoGebra Conference session: "Constructions of Particular Planar Curves Using GeoGebra”. Link to GeoGebra book referenced here: https://www.geogebra.org/m/mh9srps6
From playlist 2022 Florida GeoGebra Conference