Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space. Simply put, digitizing is replacing an object by a discrete set of its points. The images we see on the TV screen, the raster display of a computer, or in newspapers are in fact digital images. Its main application areas are computer graphics and image analysis. Main aspects of study are: * Constructing digitized representations of objects, with the emphasis on precision and efficiency (either by means of synthesis, see, for example, Bresenham's line algorithm or digital disks, or by means of digitization and subsequent processing of digital images). * Study of properties of digital sets; see, for example, Pick's theorem, digital convexity, , or digital planarity. * Transforming digitized representations of objects, for example (A) into simplified shapes such as (i) skeletons, by repeated removal of simple points such that the digital topology of an image does not change, or (ii) medial axis, by calculating local maxima in a distance transform of the given digitized object representation, or (B) into modified shapes using mathematical morphology. * Reconstructing "real" objects or their properties (area, length, curvature, volume, surface area, and so forth) from digital images. * Study of digital curves, digital surfaces, and digital manifolds. * Designing tracking algorithms for digital objects. * Functions on digital space. * Curve sketching, a method of drawing a curve pixel by pixel. Digital geometry heavily overlaps with discrete geometry and may be considered as a part thereof. (Wikipedia).
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: 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!
Complements and Supplements: Quick Conceptual Illustrator
Links: https://www.geogebra.org/m/G9De98Xv & https://www.geogebra.org/m/hXYrYnCD
From playlist Geometry: Dynamic Interactives!
Similar Figures Definition: Dynamic Illustration
Link: https://www.geogebra.org/m/EeXdSpJB
From playlist Geometry: Dynamic Interactives!
Messing with Mona: Introduction to Geometric Transformations
Link: https://www.geogebra.org/m/KFtdRvyv
From playlist Geometry: Dynamic Interactives!
Composition of 2 Line Reflections: What Can You Conclude?
Engage here: https://www.geogebra.org/m/NUtDnGgC#material/mjQyuKfG
From playlist Geometry: Dynamic Interactives!
The Two-Dimensional Discrete Fourier Transform
The two-dimensional discrete Fourier transform (DFT) is the natural extension of the one-dimensional DFT and describes two-dimensional signals like images as a weighted sum of two dimensional sinusoids. Two-dimensional sinusoids have a horizontal frequency component and a vertical frequen
From playlist Fourier
Exploring those Hard-to-Visualize Calculus 3D Surfaces
https://www.geogebra.org/m/agmkusms
From playlist Calculus: Dynamic Interactives!
Geometry Constructions by Petra Surynkova
Learn Geometry Constructions with GeoGebra! In this video series, Petra Surynkova will guide you through a variety of constructions, including bisectors, perpendiculars, and more. Follow along with her clear explanations and visual aids to master the art of geometric construction in GeoGeb
From playlist FLGGB 2023
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!
Gabriele Vezzosi - Applications of non-commutative algebraic geometry to arithmetic geometry
Abstract: We will briefly recall the general philosophy of non-commutative (and derived) algebraic geometry in order to establish a precise link between dg-derived category of singularities of Landau-Ginzburg models and vanishing cohomology, over an arbitrary henselian trait. We will then
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
Burning Bridges: Questioning Practice, Part 1
Over the two past decades, digital drawing has irrevocably transformed architectural education and practice alike. This panel assembled leading figures in digital visualization who articulate the history, opportunities, and the too often underdeveloped theoretical underpinning of this rev
From playlist 'Is Drawing Dead?' YSoA Symposium
Presented by Chris Eller, Matt Mercer, and Tassie Gniady. IU has a broad history of working with a variety of media and methods of interaction. In this session, you'll learn about two cutting-edge technologies: 360 and stereoscopic media. New 360 images and videos are available on your mob
From playlist Augmented, Virtual, and Extended Reality Seminar Series
Is 3.14 the real value of pi? NO, let’s understand this…
what is pi, 3.14? how many digits does pi have? For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes.
From playlist GED Prep Videos
Nikolaus Kriegskorte - Controversial stimuli: experiments to adjudicate computational hypotheses
Recorded 13 January 2023. Nikolaus Kriegeskorte of Columbia University presents "Controversial stimuli: Optimizing experiments to adjudicate among computational hypotheses" at IPAM's Explainable AI for the Sciences: Towards Novel Insights Workshop. Learn more online at: http://www.ipam.ucl
From playlist 2023 Explainable AI for the Sciences: Towards Novel Insights
1080 degrees around a circle with a radius of 2 cm is what distance?
How to find the circumference of a circle. Also, how to calculate arc length of angles greater than 360 degrees. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained prac
From playlist GED Prep Videos
Virtual Reality for Architectural Review
Presented by Jeff Rogers. Virtual Reality has advanced by leaps and bounds over the past few years, bringing it into the hands of more users and producers who are putting the growing medium to use. The UITS Advanced Visualization Lab presented this series on how the medium of virtual reali
From playlist Impact of Virtual Reality Seminar Series
DDPS | Machine Learning and Physics-based Simulations – Yin and Yang of Industrial Digit
Description: Combining the digital and the real world will be key to address the mega-challenges ahead of our society. Sufficiently accurate and fast digital models of assets, products, systems, and infrastructures are required to do so. This will only be achieved in the remaining time fra
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
James Maynard: Primes with missing digits
Abstract: We will talk about recent work showing there are infinitely many primes with no 7 in their decimal expansion. (And similarly with 7 replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most X1−c elements less than X) w
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Link: https://www.geogebra.org/m/ATnqfej6
From playlist Geometry: Dynamic Interactives!