- The stability of the triangle
- The one quantum created in the tetrahedron
- How the icosahedron, the octahedron and tetrahedron create everything in the universe
Few periods of ancient history sum up mathematical precision in quite as dramatic a fashion as Ancient Egypt. Against a rugged landscape of rocky mountains, rolling sand dunes, and the wide emptiness of an endless blue sky, the architects in the Land of the Pharaohs embraced geometric design with a passion by any other civilization.
The Pyramids at Giza remain one of the great architectural wonders of the world, and the giant sculpture of the Sphinx is unrivaled example of the Egyptian ability to represent the natural form within a geometric methodology. Equally interested in the mystical power of numerology were the Ancient Greeks.
With their elegant marble temples and fertile landscapes, the Greeks built a civilization of which the number three was an object of passion. Its legacy has continued to live on as a core element of more modern cultural codes and religions, suggesting that three may be more important to the way that we currently view the world than we necessarily realize.
The plurality of three offered a sense of balance, order, and geometric precision. This is something that was held with such reverence that it is present at all levels of Ancient Egyptian and Ancient Greek culture and design, including the very fabric of their buildings. Finding opportunities to include representations of the number three was a crucial element of architectural design in Greece. For instance, Doric friezes on temples feature triglyphs, which are a rectangular panel of three vertical lines.
Created by carving two angular channels (known as hemiglyphs), Greek triglyphs are thought to be a recreation of the Egyptian hieroglyph for the number three, which appears as three straight lines ( I I I ). The Doric design is thought to have represented harmony whilst invoking the powerful magic of the pluralism concept, an important consideration for a building as important as a temple.
This design remains popular today, and is a common feature of many modern skills in arts and crafts such as wood carving and metalwork. Museums frequently offer craft workshops and exhibitions exploring the exceptional skill and unique design of classical landscapes.
Such is its legacy that the triglyph is also found in many modern buildings. These include neoclassical buildings, such as those common on Broadway, and also in aspects of quintessentially modern buildings. In a nod to the civilization that gave us Democracy, the Cabinet Room, Roosevelt Room and Independence Hall of t
he White House triglyphs as part of their ceiling moldings.
It would seem that there is something irresistible about this simple representation of the number three that has caused its legacy to live on beyond the lifespan of the civilizations that created it, raising the tantalizing possibility that it will also appear in the landscapes of the distant future.
Aside from triglyphs, the number three is found in triangles throughout both Ancient Egyptian and Ancient Greek architecture. Perhaps the most overt three in Ancient Greek architecture is the triangle on the front and back of the Parthenon in Athens. Known as pediments, these triangles are considered to contain some of the finest examples of Doric sculpture, and contained images of the most important moments in the lives of the Olympic triad.
Another example of the triangle, The Great Pyramid of Giza, also features a prominent number three in the form of its three triangular faces. This is part of the complex numerology of the pyramids, the various mathematical elements of which represent the Pythagorean concept of all universal rhythms being modeled from the triangle (three), the square (four), and the pentagon (five).
Again, the triangles in Egypt are closely related to mythology, and deictic triangles in particular. The shortest side of the Pythagorean triangle (known as “Ausar”) corresponds to the Father, the longer side (known as “Auset”) corresponds to the Mother, and the hypotenuse (called “Heru”) is the son.
The power of the triangle became important amongst Ancient alchemists, and was later embraced by Medieval architects. The natural ease with which a triangle can be divided into parts whilst still remaining a whole proved an attractive idea for those who were aiming to explore the fundamental harmony of biological life.
For instance, the Egyptian Alchemical Triangle had three, four, and five divisions for the Father, Mother, and Son sides respectively. The three divisions on the Ausar side represented the three vital principles that formed the known world: salt, sulfur, and mercury, a vital part of the process of the Spirit manifesting as Matter.
The irresistible geometry of the triangle has seen the concept reappear throughout cultures and religions, making it one of the most recognized symbols in the world. Crucial to the Christian realization of the Father, Son, and Spirit trinity, the three-sided polygon also appears in Buddhism as part of the Eye of Consciousness (the so-called “third eye”), as as part of the Sri Yantra of Hinduism.
n a world where consumerism drives a fast-paced life, the importance of the fundamental building blocks of culture and civilization can easily become lost. Three may appear to be a simple number, useful for a quick bit of mental arithmetic or jotting down a phone number, but its historical importance remains all around us in the form of triangles and triglyphs.
From the ancients who truly believed in the mystical power of not simply the number three but also the concept behind it, to the geometric balance that continues to attract architects and designers to its fan club, to its integral role in constructing modern religions, the number three is a part of the ancient world that has refused to succumb to the ravages of time.
The process of learning is an important and implicit part of the users’ interaction with products, both in a digital and non-digital realm. It is a continuous process, regardless of their level of expertise or previous familiarity with the subject matter. It begins with the users’ initial interaction with the product and continues all the way through as most advanced functions and features are learned. An effective learning experience can greatly enhance the users’ overall experience with the product.
The action of learning is a three-step process, comprised of Information Acquisition, Information Processing and Information Cataloging/Action Taking. Let’s take a look at what is involved in each of these three steps.
The goal of this discussion is to explore the nature of the action of learning, as well as to define what factors ensure the most effective learning process for the user.
The action of learning is a three-step process, comprised of Information Acquisition, Information Processing and Information Cataloguing/Action Taking. Let’s take a look at what is involved in each of these three steps.
In this first step, the user receives new information from a single source or from multiple sources. This new information may be presented in a visual, auditory, or sensory format.
In the second step, the user processes the newly acquired information by acknowledging and understanding its meaning. This step is dependent on the user’s individual mental processing capabilities, which may vary from person to person. The user’s previous familiarity with similar types of information may play a significant role in his/her processing of this new information.
Having processed the newly received information the user in turn then stores it for future use by mentally cataloguing it. As part of this cataloguing process, the user creates necessary contextual associations to easily access the newly learned information at a later date. At times, as we will see shortly, the Action Taking is conducted without the need for Cataloguing.
Later in this discussion we will look at some of the factors, which provide for a more effective learning process for the user. Now, however, let’s take a look at a commonplace example, which will illustrate the three steps involved in the action of learning. I refer to this as the Traffic Light Sequence.
As the driver approaches an intersection, the traffic light changes from green to yellow; a visual cue. The driver acquires this new information and acknowledges the change in the traffic light. His/her ability to understand the meaning of this event will largely be based on previously learned information about the individual meanings of the colors of the traffic light.
Having acknowledged that the traffic light changed, the driver has to process the actual meaning of this event. The driver is aware that a certain action is needed to respond to the change in the traffic light. Other ambient factors may require additional mental tasks and calculations on the part of the driver, such as noticing the presence of the police vehicle within the driver’s peripheral vision. These ambient factors place an additional burden on the driver’s decision-making capability to take the most effective (and safe) course of action.
Having completed the information-processing task(s) the driver makes the decision to apply the brakes and come to a complete stop. This action completes the third and last step in this sequence.
The action of learning is a highly individualized process in that it varies from person to person. There are several factors that can make the learning process more effective and user-friendly.
Often highly complex, information needs to be properly formatted and presented to its intended audience in a concise and effective way. Clarity of presentation plays a critical role in the overall learning process. It is important to consider proper visual and/or audio delivery methods. Information architecture, spatial organization, layout considerations, data density and sound levels, among others things, need to be carefully considered.
To ensure effective information delivery and enhance the users’ learning experience, it is important to select and apply the most effective methods of information delivery. For example, learning new features of a digital platform may require a combination of methods, such as instructional training, online resources, collaborative workshops and user manuals. The lecture format, a popular if not somewhat outdated method of information delivery, is widely used in higher education. This form of learning requires students to understand and retain the information presented by their instructor during a lecture. There are a number of factors in the use of this information delivery format, however, that can make the students’ learning process very challenging, including the instructors’ voice, cadence, rhythm of speech, accent, physical posture, their energy level, as well as their ability to effectively hold the attention of a lecture hall.
It is not enough to simply present the new information to students; it is equally critical to effectively illustrate to students the relevance of this new information as it applies to real-world, current industry examples. This is one of the biggest factors, which, in my opinion, is often lacking in the instructional realm of academia.
Empathy is a key element of effective information delivery. This is particularly true in an interactive form as part of the instructional process. This in turn leads to a much more effective and enjoyable learning experience for the user. Understanding the holistic and conceptual framework of what they are learning, also allows them to apply new skills and information much more effectively. This is why it is very important for the instructor to not only explain the “what” and the “how,” but also the “why.”
The factors described above are equally important in both the educational and corporate environment. The latter includes departments such as Development, Operations, Product and Human Resources, where effective instructional methods play a critical role.
The more complex and advanced the information is, the greater the instructional effort needs to be made, to deliver an effective and user-friendly learning experience to a technologically and intellectually diverse audience. Available instructional resources need to be properly researched and analyzed. Appropriate content delivery methods need to be carefully selected. Moreover, the information delivery methods may need to be customized and modified, should the need arise, even during the ongoing instructional process.
In the end, such an approach will improve the users’ learning processes, ultimately enhancing their overall experience of learning.
About the author:
Twice Blessed Bridal should be called Third Time Threads.
That’s because Mitterholzer, 23, of Dayton, will wear the same dress — with a few alterations, of course — that her grandmother, Jean Beckdahl, 87, wore on April 18, 1953 when she married Walter Beckdahl in Mansfield and her mother, Lynn Mitterholzer, 57, wore on Sept. 19, 1981 when she married Doug Mitterholzer in Springfield.
Navajo Chiefs Blankets are the most recognizable and valuable of all Navajo weavings. Navajo Chiefs Blankets have been collected not only by other Native Americans before the United States even existed, but also by such notable collectors as William Randolf Hearst.
A Navajo Chiefs Blanket could be purchased for around fifty dollars in the early 1800’s, one thousand dollars by the turn of the nineteenth century, and today, a Chiefs blanket in excellent condition, could sell for half a million dollars or more.
The First Phase Navajo Chiefs Blanket is simple with indigo blue stripes and white and brown natural churro wool.
THE MOUSAI (Muses) were the goddesses of music, song and dance, and the source of inspiration to poets. They were also goddesses of knowledge, who remembered all things that had come to pass. Later the Mousai were assigned specific artistic spheres: Kalliope (Calliope), epic poetry; Kleio (Clio), history; Ourania (Urania), astronomy; Thaleia (Thalia), comedy; Melpomene, tragedy; Polymnia (Polyhymnia), religious hymns; Erato, erotic poetry; Euterpe, lyric poetry; and Terpsikhore (Terpsichore), choral song and dance.
An incredible and practical way of folding a t-shirt in less than 5 seconds! Using this method the best folders can do it in 3 seconds!
This technique for teeshirt folding, used widely in China, can be learnt in 2 minutes if you watch the video
The Bauhaus was the most influential modernist art school of the 20th century, one whose approach to teaching, and understanding art’s relationship to society and technology, had a major impact both in Europe and the United States long after it closed. It was shaped by the 19th and early 20th centuries trends such asmovement, which had sought to level the distinction between fine and applied arts, and to reunite creativity and manufacturing.
This is reflected in the romantic medievalism of the school’s early years, in which it pictured itself as a kind of medieval crafts guild. But in the mid 1920s the medievalism gave way to a stress on uniting art and industrial design, and it was this which ultimately proved to be its most original and important achievement. The school is also renowned for its faculty, which included artists, , , and , architects and , and designer .
Sandro Miller, Edward Sheriff Curtis / Three Horses (1905), 2014
From the Malkovich, Malkovich, Malkovich – Homage to photographic masters series
14 x 11″ pigment print
Edition of 35 + 5 AP’s
Three primary colors:
1 & 9 = Yellow (primary)
2 & 10 = Blue (primary)
3 & 11 = Red (primary)
Three secondary colors:
4 & 12 = Purple (blue+red)
5 & 13 = Orange (red+yellow)
6 & 14 = Green (yellow+blue)
One tertiary color:
7 & 15 = Maroon (purple+red)
Two all-or-nothing colors:
8 = Black
Cue = White