Aodh Macs Blog

The Ancient-Greek Definite Article The Definite Article: The Ancient-Greek Definite Article:      Singular: Dual: Plural:      Masculine: Feminine: Neuter: Masculine: Feminine: Neuter: Masculine: Feminine: Neuter: Nominative: ὁ ἡ τό τώ τώ , τᾱ́ τώ οἱ αἱ τά Genitive: τοῦ τῆς τοῦ τοῖν τοῖν , ταῖν τοῖν τῶν τῶν τῶν Dative: τῷ τῇ τῷ τοῖν τοῖν , ταῖν τοῖν τοῖς ταῖς τοῖς ...

Introduction to Modern Geometry Modern Geometry: The Directed Line Segment In Euclidean Geometry, line segments possess only magnitude, and not direction. A B      Figure 1:   In Euclidean Geometry, only the magnitude of line segments is considered. As we can see in Figure 1 , in Euclidean Geometry, the line segment: |AB| would be considered equal to the line segment: |BA| . However, this is not the case with Modern Geometry. In Modern Geometry, line segments not only possess magnitude, but direction also. A B      Figure 2:   In Modern Geometry, line segments possess direction as well as magnitude. In Modern Geometry: |AB| is termed: ‘a directed line segment’ . ...

There Exists There_exists_symbol      Figure 1:   A there exists symbol that I coded in SVG.      Figure 2:   The SVG code that generates the vector image depicted in Figure 1 .      Figure 3:   What the above image, depicted in Figure 1 looks like when exported as a .PNG file. I believe that I could program better if I knew more Mathematics, and — to that end — I am following some Engineering-Mathematics courses on YouTube.  For instance: the more plane and Cartesian Geometry that I learn, the better I am able to script images in SVG. The symbol depicted in Figure 1 means: There exists . You may view the source code for this there-exists symbol at my Codepen  account.

     Figure 1:   A Venn diagram that illustrates how information, or data is grouped as regards Structured Query Language. How information is grouped together within programming languages is an important concept to grasp.  I find that the drawing of Venn diagrams assists me with this.

My first X3DOM page Hello, Cube!      Figure 1:   It is possible to script Three-dimensional objects with X3DOM.  X3DOM follows the declarative scripting paradigm of two-dimensional SVG as opposed to following the programming imperative paradigm of JavaScript and Canvas. This is my first html page that includes a three-dimensional object. X3DOM is a Javascript library that allows one to code three-dimensional objects - such as cubes, speheres, cylinders, etc. - with tags, just as SVG allows one to do with two dimensional objects - squares, circles etc. You can manipulate the below cube with your finger - should you be employing a touchscreen - or with your mouse cursor - should you be employing a desktop. Should you use two fingers on a touch-screen device, then you can scale the size of the cube in real time. Holding one's two fingers to the screen...

The Phi Quadrilateral. Phi Quadrilateral a b x y c d      Figure 1:   A Phi Quadrilateral that I coded in SVG.  I believe that these are used for perspective.  The first quadrilateral will have its base line-segment at the bottom of the canvas, in the foreground.  A second quadrilateral - scaled to 0.618033988... the size of the first, will have its base equal in magnitude to the top line segment of the original quadrilateral.  This second quadrilateral has its base at the top line segment of the first quadrilateral. ...