In physics and mathematics, axiality and rhombicity are two characteristics of a symmetric second-rank tensor in three-dimensional Euclidean space, describing its directional asymmetry. Let A denote a second-rank tensor in R3, which can be represented by a 3-by-3 matrix. We assume that A is symmetric. This implies that A has three real eigenvalues, which we denote by , and . We assume that they are ordered such that The axiality of A is defined by The rhombicity is the difference between the smallest and the second-smallest eigenvalue: Other definitions of axiality and rhombicity differ from the ones given above by constant factors which depend on the context. For example, when using them as parameters in the irreducible spherical tensor expansion, it is most convenient to divide the above definition of axiality by and that of rhombicity by . (Wikipedia).
Introduction to Spherical Coordinates
This video defines spherical coordinates and explains how to convert between spherical and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Applying the properties of a rhombus to determine the length of a diagonal
๐ Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
Using the properties of a rhombus to determine the missing value
๐ Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
How to find the missing angle of a rhombus
๐ Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
Using the properties of a rhombus to determine the side of a rhombus
๐ Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
Eleftherios Pavlides & Thomas Banchoff - Hinge Elastegrities Shape Shifting - G4G12 April 2016
Named by analogy to tensegrity, maintaining form integrity through tension alone, hinge-elastegrity, maintaining form integrity with elastic hinges, is created by folding and weaving a shape-memory membrane, into a network of rigid members suspended with elastic hinges. The shape-shifting
From playlist G4G12 Videos
Introduction to Spherical Coordinates
Introduction to Spherical Coordinates This is a full introduction to the spherical coordinate system. The definition is given and then the formulas for converting rectangular to spherical and spherical to rectangular. We also look at some of the key graphs in spherical coordinates. Final
From playlist Calculus 3
Using the pythagorean theorem to a rhombus
๐ Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
Live demo https://codepen.io/thebabydino/pen/OJmmwrz If the work I've been putting out since early 2012 has helped you in any way or you just like it, please consider supporting it to help me continue and stay afloat. You can do so in one of the following ways: * you can be a cool cat ๐ผ๐ฉ
From playlist Basic Tips & Tricks
Determining acute vertical angles
๐ Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure
The cube shadow theorem (pt.2): The best hypercube shadows
NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Make sure to watch part 1 of this video before you watch part 2: https://youtu.be/rAHcZGjKVvg In this s
From playlist Recent videos
See http://thedicelab.com/ for more details. These dice are available at http://www.mathartfun.com/shopsite_sc/store/html/DiceLabDice.html
From playlist Dice
Jane Kostick - Coordinated Motion Around a Dodecahedron - G4G12 April 2016
The presentation included a demonstration of wooden sculptures that come apart in two-stages, like a coordinated motion puzzle. They are composed of four sets of a dozen sticks surrounding a 12-sided block.
From playlist G4G12 Videos
Laura Taalman - 3D printed Hinged Dissections and Foldable Polyhedra - CoM Apr 2021
Weโll talk briefly about 3D printing foldable and hinged models for polygonal and polyhedral dissections, and a new idea for โvolume netsโ for which I am seeking feedback. Included will be access to 3D design files that people can use to create their own models. Q&A at the end can extend t
From playlist Celebration of Mind 2021
The Collapse of Viruses: Graph-Based Percolation Theory in the Wolfram Language
Graph-based percolation theory may be done in the Wolfram Language, here to aid in the understanding of viruses, their disassembly and eventual collapse. Capsids are protein nanocontainers that store and protect a virusโs genetic material in transit between hosts. Capsids consist of hundre
From playlist Wolfram Technology Conference 2020
Developing the Martin Gardner Modular Origami G4G12 Rhombic Dodecahedron โ Peter Knoppers
How I designed a modular origami object for the 12th gathering for Gardner. Files available for download on http://www.buttonius.com/G4G12/
From playlist G4G12 Videos
Jane Kostick - 13-Piece Puzzles - G4G13 April 2018
Geometric constructions with 13 pieces
From playlist G4G13 Videos
Determine the values of two angles that lie on a lie with a third angle
๐ Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure