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De: BARILOCHENSE6999 Enviado: 20/04/2019 14:22
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Math in Architecture and the Golden Section

 
math in architecture

The Golden Section (aka Golden Mean, and Golden Ratio) phys.org

We use math in architecture on a daily basis to solve problems. We use it to achieve both functional and aesthetic advantages. By applying math to our architectural designs through the use of the Golden Section and other mathematical principles, we can achieve harmony and balance. As you will see from some of the examples below, the application of mathematical principles can result in beautiful and long-lasting architecture which has passed the test of time.

Using Math in Architecture for Function and Form

We use math in architecture every day at our office. For example, we use math to calculate the area of a building site or office space. Math helps us to determine the volume of gravel or soil that is needed to fill a hole. We rely on math when designing safe building structures and bridges by calculating loads and spans. Math also helps us to determine the best material to use for a structure, such as wood, concrete, or steel.

“Without mathematics there is no art.” – Luca Pacioli, De divina proportione, 1509

Architects also use math when making aesthetic decisions. For instance, we use numbers to achieve attractive proportion and harmony. This may seem counter-intuitive, but architects routinely apply a combination of math, science, and art to create attractive and functional structures. One example of this is when we use math to achieve harmony and proportion by applying a well-known principle called the Golden Section

Math and Proportion – The Golden Section

Math in Architecture

Perfect proportions of the human body – The Vitruvian Man – by Leonardo da Vinci.

We tend to think of beauty as purely subjective, but that is not necessarily the case. There is a relationship between math and beauty. By applying math to our architectural designs through the use of the Golden Section and other mathematical principles, we can achieve harmony and balance.

The Golden Section is one example of a mathematical principle that is believed to result in pleasing proportions. It was mentioned in the works of the Greek mathematician Euclid, the father of geometry. Since the 4th century, artists and architects have applied the Golden Section to their work.

The Golden Section is a rectangular form that, when cut in half or doubled, results in the same proportion as the original form. The proportions are 1: the square root of 2 (1.414) It is one of many mathematical principles that architects use to bring beautiful proportion to their designs.

Examples of the Golden Section are found extensively in nature, including the human body. The influential author Vitruvius asserted that the best designs are based on the perfect proportions of the human body.

Over the years many well-known artists and architects, such as Leonardo da Vinci and Michelangelo, used the Golden Section to define the dimensions and proportions in their works. For example, you can see the Golden Section demonstrated in DaVinci’s painting Mona Lisa and his drawing Vitruvian Man.

Famous Buildings Influenced by Mathematical Principles

Here are some examples of famous buildings universally recognized for their beauty. We believe their architects used math and the principals of the Golden Section in their design:

Parthenon

The classical Doric columned Parthenon was built on the Acropolis between 447 and 432 BC. It was designed by the architects Iktinos and Kallikrates. The temple had two rooms to shelter a gold and ivory statue of the goddess Athena and her treasure. Visitors to the Parthenon viewed the statue and temple from the outside. The refined exterior is recognized for its proportional harmony which has influenced generations of designers. The pediment and frieze were decorated with sculpted scenes of Athena, the Gods, and heroes.

Math in Architecture

Parthenon Golden Section

Notre Dame Cathedral in Paris

Built on the Ile de la Cite, Notre Dame was built on the site of two earlier churches. The foundation stone was laid by Pope Alexander III in 1163. The stone building demonstrates various styles of architecture, due to the fact that construction occurred for over 300 years. It is predominantly French Gothic, but also has elements of Renaissance and Naturalism. The cathedral interior is 427 feet x 157 feet in plan. The two Gothic towers on the west façade are 223 feet high. They were intended to be crowned by spires, but the spires were never built. The cathedral is especially loved for its three stained glass rose windows and daring flying buttresses. During the Revolution, the building was extensively damaged and was saved from demolition by the emperor Napoleon.

Math in Architecture.

Notre Dame Cathedral in Paris

Taj Mahal

Built in Agra between 1631 and 1648, the Taj Mahal is a white marble mausoleum designed by Ustad-Ahmad Lahori. This jewel of Indian architecture was built by Emperor Shah Jahan in memory of his favorite wife. Additional buildings and elements were completed in 1653. The square tomb is raised and is dramatically located at the end of a formal garden. On the interior, the tomb chamber is octagonal and is surrounded by hallways and four corner rooms. Building materials are brick and lime veneered with marble and sandstone.

Math in Architecture and the Golden Section

Taj Mahal designed by Ustad-Ahmad Lahori

As you can see from the above examples, the application of mathematical principles can result in some pretty amazing architecture. The architects’ work reflects eye-catching harmony and balance. Although these buildings are all quite old, their designs have pleasing proportions which have truly passed the test of time.

 

https://bleckarchitects.com/math-in-architecture/


Respuesta  Mensaje 19 de 32 en el tema 
De: BARILOCHENSE6999 Enviado: 04/05/2019 15:09

“Earth’s Second Sun” –China’s Fusion Future, the Holy Grail of Unlimited Energy’ (Weekend Feature)

 

Sun CME

 

On March 19, 2109 The Galaxy reported that China was close to launching its “artificial sun” promising a future of ‘limitless clean energy –a Chinese “Green New Deal”. Unlike nuclear fission, fusion emits no greenhouse gases and carries less risk of accidents or the theft of atomic material.

 

The current Experimental Advanced Superconducting Tokamak (EAST) reactor in Hefei has created temperatures as hot as the interior of the sun. In November, it became the first facility in the world to generate 100 million degrees Celsius (212 million Fahrenheit)—six times as hot as the sun’s core. These mind-boggling temperatures are crucial to achieving sustainable nuclear fusion reactions, which promise an inexhaustible energy source.

“Stupendous” –China’s Leap to Space-Based Solar Power: ‘Will Beam Sun’s Energy Back to Earth’

 

“The artificial sun’s plasma is mainly composed of electrons and ions and the country’s existing Tokamak devices have achieved an electron temperature of over 100 million degrees C in its core plasma, and an ion temperature of 50 million C, and it is the ion that generates energy in the device,” said Dr Duan Xuru, an official at the China National Nuclear Corporation, according to China’s Global Times.

HL-2M Tokamak is expected to increase the electricity intensity from one mega amperes to three mega amperes, an important step to achieve nuclear fusion, a spokesperson surnamed Liu with the press office of the Southwestern Institute of Physics (SWIP), affiliated with China National Nuclear Corporation, told the Global Times.

“The Milky Way Base” –China Names First Human-Technology Landing Site on Moon’s Far Side

 

For instance, the deuterium (also known as heavy hydrogen) extracted from one liter of seawater releases the energy equivalent of burning 300 liters of gasoline in a complete fusion reaction, Liu said.

The “artificial sun” aims to release nuclear fusion in the same way as the sun by using deuterium and tritium (radioactive hydrogen-3), and finally generate electricity. It is clean energy that will not generate waste, which makes it ideal for people to use in the future, Liu said.

https://dailygalaxy.com/2019/04/earths-second-sun-chinas-fusion-future-the-holy-grail-of-unlimited-energy-weekend-feature/



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MATT 16:18 is an in your face glyph for the golden mean ratio 1.618

(“MATT” is pun of “MATTER”)

Golden Mean ratio of 1.618

Golden Mean ratio of 1.618

The Golden Meand and the Equilateral Triangle in a Circle

The Golden Mean and the Equilateral Triangle in a Circle; THE CRUCIAL FACT IS THE MIDPOINT OF THE TRIANGLE SIDE

Star Tetrahedron, formed by the MIDPOINTS OF THE CENTRAL EQUILATERAL TRIANGLE

Star Tetrahedron, formed by the MIDPOINTS OF THE CENTRAL EQUILATERAL TRIANGLE  (the blue and rose colored lines indicate these midpoint halves)

 
 
 
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Saint Mary Magdalene in Venice

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De: BARILOCHENSE6999 Enviado: 04/04/2025 16:33

The Tesla Coil Through Time

·
·

How it came to be and why.

Nikola Tesla was a unicorn person before “unicorn person” became a term.

He was a Serbian inventor who came up with the idea of wireless energy transfer among things like alternating current, induction motors and many others.

I would say that he built out his idea of global wireless energy transfer in three phases. The very first was the Tesla Coil, which I made a video about. You can check it out below.

 

The second phase of his scaling plan was when he built the Magnifying Transmitter. He built this at his laboratory in Colorado Springs.

This was essentially a larger version of the Tesla Coil. Using it as an analogy, the first tower represents the primary coil, and the second tower represents the secondary coil.

Finally, the third phase of his scaling was to take it global. He planned and built out the Wardenclyffe Tower in New York.

However, this version failed and was eventually taken down in 1917, but we’re getting ahead of ourselves. Let’s take a look at what needed to happen before Tesla came up with his very first demonstration; the Tesla Coil.

Historical Beginnings

To explain Tesla’s journey towards global wireless energy transfer, there are a few key points in history and inventions that we need to go over first.

The first key invention is that of the battery in the 1780s. Two physicists, Galvani and Volta, conducted an experiment. I talk about the entire process in my article about the physics behind wireless energy transfer. I’ve linked it below.

Following the battery, a Danish physicist named Hans Christian Ørsted learned that a moving electric current creates a magnetic field. His discovery was the first to find the link between electricity and magnetism. He demonstrated this in a lecture in 1820.

Perhaps the most important invention hereafter for the Tesla Coil is the electromagnet. In 1826, William Sturgeon, an English physicist, discovered that electric current running through a wire coiled around an iron bar caused the iron bar to behave like a magnet.

He fittingly named this the electromagnet.

A few years later in 1831, a man named Michael Faraday wondered if he could make electricity with magnets. So, he used electromagnets. Faraday is most well known for discovering electromagnetic induction.

He used two separate coils wrapped around one iron ring and noticed that when he attached/disconnected a battery to the first wire, the second wire would get a jolt of electricity. He called this inducing a current.

This phenomenon is explained using Faraday’s Law of Induction, which states that:

a changing magnetic field will induce an electromotive force (EMF) in a loop of wire, where EMF is what causes electrons to move and form a current

At this point, all of the components necessary to conceive of the Tesla Coil had been invented, but the background doesn’t end here.

What Was Innovated?

Following Faraday’s discovery of induction, Nicholas Callan, an Irish priest, wanted to improve Faraday’s device.

He decided to wind both the primary and secondary coils around the same iron bar while keeping them electrically separate. Doing this allowed him to feel electrical jolts from wire that had not been directly connected to a battery!

He also found that if the primary wire, the one connected to the battery, was thick and that the secondary wire was thin and had been coiled more, the jolt produced was more powerful.

If the secondary coil has fewer loops than the primary coil, the result is more current and less voltage. However, Callan’s made a secondary coil with more loops than the primary coil, so the result was more voltage and less current.

Callan’s device was named the Step-Up Transformer. When he connected the battery to a coil, it became an electromagnet with a magnetic field. When he disconnected the battery, it lost its magnetic field.

Using Faraday’s Law, every time Callan connected or disconnected, he created a new current in the second coil of wire. He also used a wheel to mechanically connect and disconnect the battery, acting as a kind of “repeater.”

Though this version was later improved by William Sturgeon, Callan’s device was used for electroshock therapy for many years.

The biggest advancement thereafter was using the coil itself to disconnect and connect to the battery instead of using the wheel. How did this work?

Well, the current running through the primary coil caused it to behave like a bar magnet. The wire carrying the current was then connected to a switch so that it could pull on it and activate a spring in the circuit.

The movement of the spring would turn off the current. However, once the connection was removed, the primary coil would no longer be magnetic. This causes the spring to disconnect, and the switch to turn back on.

An Electrical Interrupter

This process of the switch turning on and off would click about 20 to 40 times per second and was named an electrical interrupter.

There was still room for innovation.

The electrical interrupter would sometimes spark. So, in 1853 a man named Armand Fizau created the Leyden Jar to absorb the spark. It was the first version of a capacitor.

This is something made of two large conducting materials separated by insulating material.

By adding the capacitor and getting rid of the spark, Fizau created a new device — one that took DC from a battery and made bursts of AC in the 1850s.

Though not necessary to understanding the Tesla Coil, I’ll mention too that in 1886, Heinrich Hertz added an antenna to the induction coil and created the first man-made radio wave.

This is where Tesla comes in.

Tesla’s Take

Having heard of the radio waves created by Hertz, Tesla visited the World Fair in Paris, 1889. He began tinkering with the induction coil. Among other things, he removed the interrupter and DC battery and replaced it with an AC generator.

This makes sense — why use a battery and mechanical switch to turn the current on and off when a generator that automatically switches the current’s direction could be used instead?

Though this first adaptation didn’t actually work out at the end (due to overheating and melting of wire insulation) it did lead to Tesla’s use of a spark or air gap.

With a few other tweaks, we finally arrive at the original version of the Tesla Coil which looked something like this:

The Original Tesla Coil Circuit Uses Capacitors and Spark Gaps

The modern version, which is what I recreated in my video, is slightly simpler. It no longer uses capacitors or spark gaps and looks like this:

Modern Version of the Tesla Coil Circuit

P.S. for an explanation of how electromagnetic induction works in the modern circuitry, watch my video linked near the beginning of this article.

Nikola Tesla wirelessly lit up a bulb in the year 1891 using his coil, but as I said earlier, his dream was to send wireless power over large distances by using the earth.

After the Tesla Coil worked, he built the larger version that I mentioned earlier called the Magnifying transmitter. It was able to light up three incandescent bulbs at 100ft or 30metres away.

Following his second success, he built the Wardenclyffe Tower in Long Island in 1901. He wanted to use the tower to harness the energy that he thought was inside Earth, in the hopes of turning our planet into a gigantic dynamo.

The tower would take energy from a coal-power generator and send it deep into the ground with a metal rod. He thought that the Earth’s crust would transport the energy.

The tower, however, was considered a failure, was taken down in 1917 and never finished. There are many speculations as to why it didn’t work, some more sound than others, of course.

The article I’ve linked below does a great job of explaining some of the flaws of the tower and how Tesla tried to address

There’s a lot left for us to develop when it comes to modern-day wireless energy transfer. We’ve only scratched the service, even with other methods like radio wave transmission and inductive coupling. To read more about how wireless energy transfer looks now, read this article I wrote.

   

TLDR;

  • Previous inventions including the battery, electromagnet, induction theory and capacitors were all necessary precursors to the Tesla Coil
  • Tesla’s ideation of the coil is based on the principles of electromagnetic induction — a form of wireless energy transfer that we continue to build on now with things like wireless phone charging plates etc.
  • He tried to scale the coil by building the Magnifying Transmitter then the Wardenclyffe Tower
   

If you enjoyed this article, be sure to give it a few ????s and follow me on Medium!

https://ruhani-walia.medium.com/the-tesla-coil-through-time-611067b97019


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