In abstract algebra, a medial magma or medial groupoid is a magma or groupoid (that is, a set with a binary operation) which satisfies the identity , or more simply for all x, y, u and v, using the convention that juxtaposition denotes the same operation but has higher precedence. This identity has been variously called medial, abelian, alternation, transposition, interchange, bi-commutative, bisymmetric, surcommutative, etc. Any commutative semigroup is a medial magma, and a medial magma has an identity element if and only if it is a commutative monoid. The "only if" direction is the Eckmann–Hilton argument. Another class of semigroups forming medial magmas are normal bands. Medial magmas need not be associative: for any nontrivial abelian group with operation + and integers m ≠ n, the new binary operation defined by yields a medial magma which in general is neither associative nor commutative. Using the categorical definition of product, for a magma M, one may define the Cartesian square magma M × M with the operation (x, y) ∙ (u, v) = (x ∙ u, y ∙ v) . The binary operation ∙ of M, considered as a mapping from M × M to M, maps (x, y) to x ∙ y, (u, v) to u ∙ v, and (x ∙ u, y ∙ v) to (x ∙ u) ∙ (y ∙ v) .Hence, a magma M is medial if and only if its binary operation is a magma homomorphism from M × M to M. This can easily be expressed in terms of a commutative diagram, and thus leads to the notion of a medial magma object in a category with a Cartesian product. (See the discussion in auto magma object.) If f and g are endomorphisms of a medial magma, then the mapping f∙g defined by pointwise multiplication is itself an endomorphism. It follows that the set End(M) of all endomorphisms of a medial magma M is itself a medial magma. (Wikipedia).
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From playlist GeoGebra Geometry
How to find the volume of an oblique pyramid
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
Finding the volume and surface area of a pyramid with a rectangular base
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
Similarity in Right Triangles (I)
Link: https://www.geogebra.org/m/fswR8fRV
From playlist Geometry: Dynamic Interactives!
Introducing the Concept of Congruence
From playlist GeoGebra Geometry
Dodecahedron in Geogebra Step by step tutorial on this link: https://youtu.be/FPDOfPhheFk In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
Writing Equivalent Polar Coordinates Quiz
Link: https://www.geogebra.org/m/MxAvq5Yt
From playlist Trigonometry: Dynamic Interactives!
Ellen Gasparovic 8/12/20 The medial axis: Image analysis, homological simplification, gerrymandering
Title: The medial axis in image analysis, the homological simplification problem, and gerrymandering Abstract: In this talk, we will discuss three different applications of the medial axis. First, in joint work with Erin Chambers and Kathryn Leonard, we propose a method for segmenting obj
From playlist AATRN 2020
ANATOMY FOR ARTISTS: The Foot-Triangular foot wedge diagram drawing
Marc demonstrates drawing triangular foot wedges or volumetric feet using the skeleton as a reference point.
From playlist ANATOMY FOR ARTISTS
Memory (Part 2) || Cognitive Neuroscience (PSY 315W)
This is a recorded version of a livestream distance learning lecture, recorded during the coronavirus pandemic of 2020. Topics include: amnesia, Clive Wearing, H. M., medial temporal lobe, explicit memories, and hippocampus. I claim no ownership over any music, videos, or advertisements
From playlist Cognitive Neuroscience Lectures
ANATOMY FOR ARTISTS: The Upper Arm-MUSCLES
Marc draws and demonstrates the relevant muscles of the upper arm.
From playlist ANATOMY FOR ARTISTS
Lecture 20: Geodesics (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Remembering and the Brain: Can Brain Scans Detect Memories?
(October 23, 2009) Stanford Professor of psychology and neuroscience, Anthony Wagner PhD, discusses how the brain supports memory for everyday events, and will evaluate whether "mind reading" with brain imaging can detect when a person remembers the past and how this might be used as evide
From playlist Reunion Homecoming
ANATOMY FOR ARTISTS: The Foot-Bones of the feet
All 26 bones of the foot are described generally for drawing purposes.
From playlist ANATOMY FOR ARTISTS
Euler's line proof | Special properties and parts of triangles | Geometry | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/triangle-property-review/v/euler-s-line-proof Proving the somewhat mystical result that the circumcenter, centroid and orthocent
From playlist Special properties and parts of triangles | Geometry | Khan Academy
ANATOMY FOR ARTISTS: Full Feet and Toes-Muscle & Bone: PART 1
Marc uses art historical sculptures (feet) to describe and draw foot anatomy in sketch form.
From playlist ANATOMY FOR ARTISTS
How to find the volume of a pentagonal pyramid
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
ANATOMY FOR ARTISTS: Bones of the Lower Leg-Tibia and Fibula
Marc describes and draws the lower leg bones-Tibia and Fibula and discusses their importance and relevance in human anatomy and figure drawing. (This is a better version video than the one recorded prior.)
From playlist ANATOMY FOR ARTISTS