Sesquiquadrate⚼135°(also known as the "sesquisquare," "square-and-a-half," and/or "trioctile")

The glyph of the Semi-Square under the glyph of the Square, implying the sum of them both

BIG FOUR ASTEROIDS  After the first four asteroids were discovered, there wouldn't be another discovered for 38 years (Astraea). The first four gained popularity as full-fledged planets, but the rapid development of telescopes led to new asteroids being frequently discovered in what is now known as the main-belt. Some astronomers grouped the first 10 asteroids alongside the first four asteroids as planets until the reclassification that was decided upon after the discovery of Hygiea, the 10th known asteroid.


In modern times, however, the assignment of decans has changed considerably. Each sign is allocated a triplicity, such as airwaterearth or fire. Each sign is therefore subdivided into three equal parts of 10 degrees each, and these parts are referred to as decans, or decanates.

The asterisms are divided into four groups


Ancient Chinese astronomers divided the sky ecliptic into four regions, collectively known as the Four Symbols, each assigned a mysterious animal. They are Azure Dragon (青龍) on the east, Black Tortoise (玄武) on the north, White Tiger (白虎) on the west, and Vermilion Bird (朱雀) on the south. Each region contains seven mansions, making a total of 28 mansions. These mansions or xiù correspond to the longitudes along the ecliptic that the Moon crosses during its 27.32-day journey around the Earth and serve as a way to track the Moon's progress. In Taoism they are related to 28 Chinese generals.[5]

The twenty-eight mansions of the Chinese astronomy


This is principally shown by their sacred ceremonial. For first advances the Singer, bearing some one of the symbols of music. For they say that he must learn two of the books of Hermes, the one of which contains the hymns of the gods, the second the regulations for the king's life. And after the Singer advances the Astrologer, with a horologe in his hand, and a palm, the symbols of astrology. He must have the astrological books of Hermes, which are four in number, always in his mouth.

In the paper “A new four-scroll chaotic attractor consisted of transient chaotic two-scroll and ultimate chaotic two-scroll,” Y. Xu et al. used the feedback controlling method to find a new four-scroll chaotic attractor. The novel chaotic system can generate four scrolls two of which are transient chaotic and the other two of which are ultimate chaotic. Of particular interest is that this novel system can generate one-scroll, two 2-scroll, and four-scroll with variation of a single parameter. We analyze the new system by means of phase portraits, Lyapunov exponents, fractional dimension, bifurcation diagram, and Poincaré map, respectively. The analysis results show clearly that this is a new chaotic system which deserves further detailed investigation.


Under the right conditions, chaos spontaneously evolves into a lockstep pattern. In the Kuramoto model, four conditions suffice to produce synchronization in a chaotic system. Examples include the coupled oscillation of Christiaan Huygens' pendulums, fireflies, neurons, the London Millennium Bridge resonance, and large arrays of Josephson junctions.[32]

are sometimes called Jerk equations. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behaviour. This motivates mathematical interest in jerk systems. Systems involving a fourth or higher derivative are called accordingly hyperjerk systems.[31]


Four Characteristics of Dynamical Systems

Now, having explained the important tools of DST (phase space, attractors, the bifurcation diagram, and fractals), we can question what is characteristic of dynamical systems. Katherine Hayles points out four characteristics of dynamical systems: 1) non-linearity, 2) feedback mechanisms, 3) sensitivity to initial conditions, and 4) complex forms (giving rise to the importance of scale) (1990, 11-15). We have already touched on each of these characteristics in our explication of DST, so let us now simply review these with elaboration added where required. It will be noticed that these characteristics are interrelated.

Then, if we increase the control parameter beyond 3.4495, another bifurcation will occur, resulting in four possible courses for the system. Raising birthrate again past 3.56, still another bifurcation will occur, resulting in eight outcome basins. At 3.596 another bifurcation will occur, this time resulting in sixteen values that the system will equivocate between. And then, when the birthrate reaches 3.56999, the number of possibilities for the system explodes to infinity. At this point there is little, if any, predictability. The system at this point is characterized with the strange attractor.

Indeed, the bifurcation diagram corresponds to each of the attractors at different stages of systemic development. Before the first bifurcation, the system gravitates toward a point attractor. After the first bifurcation, the system gravitates toward the limit cycle attractor. After the second bifurcation, a torus attractor applies. The third and fourth bifurcations bring a torus attractor with increased dimensionality. And finally, after the last bifurcation at 3.56999, the strange attractor applies.

In this section, we look at four distinct attractors and consider the problem of identifying some of their prop- erties. 


The Science of Chaos has discovered four basic Cosmos Attractors: Point Attractor | Cycle Attractor | Torus Attractor | Strange Attractor.

Although known as the four “chaos attractors,” they are really the opposite – they are Cosmos Attractors that balance chaos. The four “Attractors” bring order out of Chaos. They are part of a basic law of four – a “fractal of four.” The Universe has a fundamental pattern of fourfoldness throughout all scales of magnitude. When applied to Nature, including Man, the Law of Four manifests as the four attractors. These attractors balance entropy, providing order from out of chaos. When applied in the microcosmic level “the four” manifests as the four basic energies or forces: electro-magnetic, gravity, and the strong and weak forces. In human consciousness its the four functions of sensing, thinking, feeling and willing. Understanding how the Attractors work in the meso-cosmic world can help us make sense of our world, and make sense of our consciousness functions.

Everywhere we see a hidden order and similarity over scales, such as is that shown geometrically by the Mandelbrot and Julia sets. This hidden order is based on one of the four Attractors, the Strange Attractor. It governs the fourth dimension of space-time reality. The other three attractors, which likewise bring hidden order out of Chaos, follow the first, second and third dimensions, the line, plane and solid. They are called the Point Attractor, the Circuit (or sometimes Cycle) Attractor and the Torus Attractor. As humans living in the fourth dimension we are at our best when we avoid their influences and follow the spontaneity and freedom of the Strange Attractor. Only in this way can we live autonomously in the moment, in tune with what the Chinese call the Tao, the Way, the flow of forces in the fourth dimension.

The four attractors act on all levels of reality to form Cosmos out of Chaos. They make up a newly discovered Wisdom Law fundamental to making sense of what is happening in the real world. The world is not really totally ordered as previously believed. It is fundamentally disordered, chaotic, but it contains forces or attractors of cosmos that create patterns of order over time. They are anchors of order in an otherwise stormy sea. Full understanding of the Attractors requires a new understanding of space and time. As to space, we need to understand how space is the original force – in Sanskrit called Brahman, in Chinese Wu Chi, in Peruvian and Japanese Ki – which creates the world through the point. Real insight into this only comes from direct experience of Ki. A new understanding of time entails realization that time is not really defined by the clock, but by intensity and rhythms. In the fields of the four attractors it is time which makes it possible for order to appear from chaos.

In the computer the electric current automatically creates the iteration. With Man it is not so easy, we ourselves have to return to Zero – Awareness – to start a new iteration. Awareness is sacred space (called “Wakan” by the Native American Lakota tribe; “Mana” by the Polynesians) which you connect with as soon as you attain the center of your true Self, called by the Japanese – Hara. Thus the difficulty which many scientists have in understanding Chaos is not mental, but existential. Their consciousness based on the Cycle attractor of analytical thinking refuses the Strange attractor, which means total individual responsibility. They cannot ground themselves in Zero and experience the true meaning of space and time. As they cannot find their inner core – Awareness/God – they can only see Chaos from the outside. They cannot make the jump from knowledge to Wisdom, to inside the black. Without this anchor they lack the experiential insight – and the confidence and Wisdom this brings – needed to live on the edge where great discoveries are made. They only see isolated Cantor sets and miss the pattern which only comes from awareness of the whole, the Mandelbrot fractal.

The Four Chaos Attractors:

  • Point Attractor

  • Cycle Attractor

  • Torus  Attractor

  • Strange Attractor The programmable unijunction transistor, or PUT, is a multi-junction device that, with two external resistors, displays similar characteristics to the UJT. It is a close cousin to the thyristor and like the thyristor consists of four p-n layers. 

Bipolar transistors have four distinct regions of operation, defined by BJT junction biases.

Forward-active (or simply active)

The base–emitter junction is forward biased and the base–collector junction is reverse biased. Most bipolar transistors are designed to afford the greatest common-emitter current gain, βF, in forward-active mode. If this is the case, the collector–emitter current is approximately proportional to the base current, but many times larger, for small base current variations.

Reverse-active (or inverse-active or inverted)

By reversing the biasing conditions of the forward-active region, a bipolar transistor goes into reverse-active mode. In this mode, the emitter and collector regions switch roles. Because most BJTs are designed to maximize current gain in forward-active mode, the βFin inverted mode is several times smaller (2–3 times for the ordinary germanium transistor). This transistor mode is seldom used, usually being considered only for failsafe conditions and some types of bipolar logic. The reverse bias breakdown voltage to the base may be an order of magnitude lower in this region.


With both junctions forward-biased, a BJT is in saturation mode and facilitates high current conduction from the emitter to the collector (or the other direction in the case of NPN, with negatively charged carriers flowing from emitter to collector). This mode corresponds to a logical "on", or a closed switch.


In cut-off, biasing conditions opposite of saturation (both junctions reverse biased) are present. There is very little current, which corresponds to a logical "off", or an open switch.

In semiconductor device fabrication, the various processing steps fall into four general categories: deposition, removal, patterning, and modification of electrical properties.

  • Deposition is any process that grows, coats, or otherwise transfers a material onto the wafer. Available technologies include physical vapor deposition (PVD), chemical vapor deposition (CVD), electrochemical deposition (ECD), molecular beam epitaxy (MBE) and more recently, atomic layer deposition (ALD) among others.

  • Removal is any process that removes material from the wafer; examples include etch processes (either wet or dry) and chemical-mechanical planarization(CMP).

  • Patterning is the shaping or altering of deposited materials, and is generally referred to as lithography. For example, in conventional lithography, the wafer is coated with a chemical called a photoresist; then, a machine called a stepper focuses, aligns, and moves a mask, exposing select portions of the wafer below to short wavelength light; the exposed regions are washed away by a developer solution. After etching or other processing, the remaining photoresist is removed by plasma ashing.

  • Modification of electrical properties has historically entailed doping transistor sources and drains (originally by diffusion furnaces and later by ion implantation). These doping processes are followed by furnace annealing or, in advanced devices, by rapid thermal annealing (RTA); annealing serves to activate the implanted dopants. Modification of electrical properties now also extends to the reduction of a material's dielectric constant in low-k insulators via exposure to ultraviolet light in UV processing (UVP).

Historically, the metal wires have been composed of aluminum. In this approach to wiring (often called subtractive aluminum), blanket films of aluminum are deposited first, patterned, and then etched, leaving isolated wires. Dielectric material is then deposited over the exposed wires. The various metal layers are interconnected by etching holes (called "vias") in the insulating material and then depositing tungsten in them with a CVD technique; this approach is still used in the fabrication of many memory chips such as dynamic random-access memory (DRAM), because the number of interconnect levels is small (currently no more than four).

Gate-all-around FETs are similar in concept to FinFETs except that the gate material surrounds the channel region on all sides. Depending on design, gate-all-around FETs can have two or four effective gates. Gate-all-around FETs have been successfully characterized both theoretically and experimentally.[34][35] They have also been successfully etched onto InGaAs nanowires, which have a higher electron mobility than silicon.[36]

The Regency TR-1 was announced on October 18, 1954 by the Regency Division of I.D.E.A., was put on sale in November 1954, and was the first practical transistor radio made in any significant numbers. Billboard reported in 1954 that "the radio has only four transistors. One acts as a combination mixer-oscillator, one as an audio amplifier, and two as intermediate-frequency amplifiers."[13] One year after the release of the TR-1 sales approached the 100,000 mark. The look and size of the TR-1 was well received, but the reviews of the TR-1's performance were typically adverse.[12] The Regency TR-1 is patented by Richard C. Koch, US 2892931, former Project Engineer of I.D.E.A.

When a split supply (dual power supply) is available, this biasing circuit is the most effective, and provides zero bias voltage at the emitter or collector for load. The negative supply VEE is used to forward-bias the emitter junction through RE. The positive supply VCC is used to reverse-bias the collector junction. Only two resistors are necessary for the common collector stage and four resistors for the common emitter or common base stage.

Transistor utilizes an isometric point of view. The player controls the character Red as she travels through a series of locations, battling enemies known collectively as the Process in both real-time combat and a frozen planning mode referred to as "Turn()". Using Turn() drains the action bar, which refills after a short delay. Until it is full again, Red cannot use Turn(), or any other ability (without a specific upgrade).[5] Red earns experience points after each battle, and may collect new powers (called Functions) from fallen victims of the Process. Functions may be equipped as one of four unique techniques, as an enhancement on another, equipped technique, or as a passive, persistent effect during battle. For example, the Function Spark() may be used to fire a wide area attack, equipped on another Function to increase its area of effect, or used as a passive effect to spawn decoys of Red. Red can also collect and activate Limiters, which serve as optional debuffs during combat, but in turn increase experience gained. Both Functions and Limiters reveal minor parts of the story if used for a long enough time.

  1. "Four Hours in Washington" – 3:01



N-type metal-oxide-semiconductor logic uses n-type field effect transistors (MOSFETs) to implement logic gates and other digital circuits. These nMOS transistors operate by creating an inversion layer in a p-type transistor body. This inversion layer, called the n-channel, can conduct electrons between n-type"source" and "drain" terminals. The n-channel is created by applying voltage to the third terminal, called the gate. Like other MOSFETs, nMOS transistors have four modes of operation: cut-off (or subthreshold), triode, saturation (sometimes called active), and velocity saturation.

FOUR OF THEM–transistor_logic

To solve the problem with the high output resistance of the simple output stage the second schematic adds to this a "totem-pole" ("push–pull") output. It consists of the two n-p-n transistors V3 and V4, the "lifting" diode V5 and the current-limiting resistor R3 (see the figure on the right). It is driven by applying the same current steering idea as above.

When V2 is "off", V4 is "off" as well and V3 operates in active region as a voltage follower producing high output voltage (logical "1").

When V2 is "on", it activates V4, driving low voltage (logical "0") to the output. Again there is a current-steering effect: the series combination of V2's C-E junction and V4's B-E junction is in parallel with the series of V3 B-E, V5's anode-cathode junction, and V4 C-E. The second series combination has the higher threshold voltage, so no current flows through it, i.e. V3base current is deprived. Transistor V3 turns "off" and it does not impact on the output.

In the middle of the transition, the resistor R3 limits the current flowing directly through the series connected transistor V3, diode V5 and transistor V4 that are all conducting. It also limits the output current in the case of output logical "1" and short connection to the ground. The strength of the gate may be increased without proportionally affecting the power consumption by removing the pull-up and pull-down resistors from the output stage.[17][18]

The main advantage of TTL with a "totem-pole" output stage is the low output resistance at output logical "1". It is determined by the upper output transistor V3 operating in active region as an emitter follower. The resistor R3 does not increase the output resistance since it is connected in the V3 collector and its influence is compensated by the negative feedback. A disadvantage of the "totem-pole" output stage is the decreased voltage level (no more than 3.5 V) of the output logical "1" (even if the output is unloaded). The reason of this reduction are the voltage drops across the V3 base–emitter and V5 anode–cathode junctions.

Planck’s constant h, and the Pythagorean symbol of mysticism π. During the course of his life, the fine-structure constant appealed to Pauli as a symbolic integer number, a theoretical coincidence, a kernel with quaternity components, and as a symbol of mystical foreboding. It had captured his attention already by the time he published his encyclopedia article on relativity theory in 1921. The visualizable kernel formed by the quaternity of e, c, h, and π, however, eluded Pauli. He never indicated that he had gleaned an image of it, nor did he decipher the mystery of the interconnectedness that he associated with the number 137.

We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangean using the Feynman sum over histories. A Schrödinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.


The MIT "space-cadet keyboard", an early keyboard with a large number of modifier keys. It was equipped with four keys for bucky bits("control", "meta", "hyper", and "super"); and three shift keys, called "shift", "top", and "front".

The English alphanumeric keyboard has a dedicated key for each of the letters A–Z, along with keys for punctuation and other symbols. In many other languages there are additional letters (often with diacritics) or symbols, which also need to be available on the keyboard. To make room for additional symbols, keyboards often have what is effectively a secondary shift key, labeled AltGr (which typically takes the place of the right-hand Alt key). It can be used to type an extra symbol in addition to the two otherwise available with an alphanumeric key, and using it simultaneously with the Shift key may even give access to a fourth symbol. On the visual layout, these third-level and fourth-level symbols may appear on the right half of the key top, or they may be unmarked.

Here it is the right-hand shift key that is smaller. Furthermore, the space bar and backspace key are also smaller, to make room for four additional keys.

A computer or standard typewriter keyboard, on the other hand, has four banks of keys, with home row being second from bottom.


The staggering of the four rows of keys comes from the manual typewriter's mechanical design. Each key is on an arm with all arms laid out in a plane at the same distance apart from one-another. The key-arms are linked to arms with typing elements laid out in the same order. 



As with three-of-a-kind there are slightly different strategies depending on whether a player is simply trying to get a four-of-a-kind or he is trying to maximize his average score. Different strategies will also be required should he need to achieve a specific target.

The strategy to maximize his chance of getting a four-of-a-kind involves keeping any four-of-a-kind that he has. If he has a four-of-a-kind then after the first throw he will keep the other if it is a 5 and 6, while after the second throw he will keep it if it is a 4, 5 or 6. So that with 22223 he keeps 2222 and will throw the 3. If he does not have a four-of-a-kind, the player should keep any three-of-a-kind or pair that he has and re-roll the other dice. With two pairs he will keep the higher pair. With no pair he will keep the highest die. Following this strategy gives him a 29.08% chance of getting a four-of-a-kind.

As with three-of-a-kind this strategy does not maximize the average score since there are a few situations after the first throw, where it is better to keep other combinations. For instance, after throwing 11166, keeping 111 maximizes the chance of getting a four-of-a-kind but keeping 66 maximizes the expected average score (6.20 rather than 4.18). The situations where the strategy to maximize the average score differs are all after the first throw and are as follows: keep 44, 55, 66 rather than 111, keep 4, 5 or 6 rather than 11, keep 6 rather than 22. Following the strategy to maximize the average score he will get a four-of-a-kind 27.74% of the time and score an average of 5.61.


Examples of bosons include fundamental particles such as photonsgluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the recently discovered Higgs boson, and the hypothetical graviton of quantum gravity. Some composite particles are also bosons, such as mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, mass number = 2), helium-4, or lead-208[Note 1]; as well as some quasiparticles (e.g. Cooper pairsplasmons, and phonons).[4]:130


The delta is a baryon which contains only up and down quarks. The Δ+ and Δ0 have the same quark compositions as the proton and neutron respectively and decay quickly by the strong interaction to the proton and neutron and a π0. If such a decay pathway is available to a particle, it decays very quickly - on the order of 10-23 seconds. Another example is the decay Δ0 --> p+ + π-. Note that the delta baryon Δ0 has the same quark makeup as the neutron, but its mass is much larger. Its mass is sufficient for this decay to be energetically favorable. The four varieties have similar masses and are said to be an isospin quartet. 


The Delta baryons are a spin excitation of the nucleon doublet. Since the nucleon is the non-strange isospin-1/2 group in the JP = 1/2+ octet (ground state), the Delta resonances are the spin-excited equivalent in the JP = 3/2- decuplet. While the nucleon will have two quark spins aligned and one opposite, and hence only two possible flavor states (uud, udd) corresponding to isospin-1/2, the Delta baryons will have all three quark spins aligned. This allows for the isospin to extend to 3/2 for the Delta's, so there are four possible flavor states (uuu, uud, udd, ddd). The bag model gives a good estimate for the masses of the Delta's in relation to the nucleons, and so does the basic vector-gluon exchange model, both with simple expressions. 



where the Ci(μ) are Wilson coefficients containing information on the heavy fields that have been integrated out and the 10 four-quark operators constructed with the light degrees of 

The most recent estimate of direct CP violation in K decays within the large Nc frame-

work is the one in [90], in which the results in [82] are also used. They calculated O(Nc2 nf ) Nc

unfactorized contributions to the dominant hadronic matrix element and find that they are large, even larger than the factorized contribution in the case of Q6. The four-point functions necessary to evaluate such kind of contributions are described using a minimal hadronic approximation for the large Nc spectrum, that in this case consists in a vector 


[12, 13, 14, 15, 16]. The Standard Model Lagrangian can be divided into four parts


= L H ( φ ) + L G ( W , Z , G ) +

Higgs Gauge
+ gψψ ̄



ψ ̄ i D/ ψ ψ=fermions




ψφψ .




Fermionic-matter content is described by leptons and quarks which are organized in three generation with two quark flavours (u and d like) and two leptons (neutrino and electron-like) each one: 



Because of this, and some absorption of constants into the fermion fields, all the parameters in the Us are con- tained in only four components of the Cabibbo-Kobayashi-Maskawa matrix Vq =UuUd† and four components of the

lνe† ql Pontecorvo-Maki-Nakagawa-Sakata matrix V =U U . The unitary matrices V and V are often parameterized as



The CKM-matrix VCKM [40, 41] is a general complex unitary matrix so, in principle, it should depend on 9 real parameters. However, part of these independent parameters can be eliminated by performing a redefinition of the phases of the quark fields. The

1.1 Overview of the Standard Model 11

matrix VCKM thus contains four independent parameters, which are usually parametrized as three angles (θ12, θ13 and θ23) and one phase δ13. The Particle Data Group preferred parametrization, the standard parametrization, is [22] 




The tetrad formalism is an approach to general relativity that replaces the choice of a coordinate basis by the less restrictive choice of a local basis for the tangent bundle, i.e. a locally defined set of four linearly independent vector fields called a tetrad.[1]

In the tetrad formalism all tensors are represented in terms of a chosen basis. (When generalised to other than four dimensions this approach is given other names, see Cartan formalism.) As a formalism rather than a theory, it does not make different predictions but does allow the relevant equations to be expressed differently.


The Utopian Impulse: Buckminster Fuller and the Bay Area, currently on view at San Francisco Museum of Modern Art (SFMOMA), focuses on the legacy of Fuller’s comprehensive global thinking as it has percolated locally in the San Francisco Bay Area. There are innumerable possibilities for curating exhibitions from Fuller’s oeuvre. Curator Jennifer Dunlop Fletcher has assembled an elegant combination of commemorative media reaching as far back as Fuller’s 1936 telegram to artist Isamu Noguchi—explaining his ideas for a Floating Tetrahedral City in the San Francisco Bay—and as far forward as to include contemporary projects inspired by Fuller, one of which was commissioned especially for this show.


Fuller had been picking up steam right along, and by this time he was talking very rapidly. Pausing to take a Japanese felt-tipped pen from his pocket, he proceeded to illustrate the next phase of the lecture with vigorous drawings on a white pad. “Now, if I’m going to subdivide the universe with triangles, how many triangles will it take to give me a system that will have both an inside and an outside?” he asked. “I found that two triangles just fall back on each other and become congruent. I found that it takes a minimum of three triangles around a point. When you put in three triangles, with three common sides, around a point, they form a fourth triangle at the base and what you get is a tetrahedron. We know that nature always does things in the simplest and most efficient way, and structures based on tetrahedrons are the structures that nature uses—these are the only babies that count. All the metals are made up of some form of tetrahedron. All the other shapes you find in nature are only transformable states of the tetrahedron. This is what nature is really doing.


Fuller started to remove his clothes, laying them out carefully on the warm, jagged rocks, which he identified for me as the top of the Allegheny range and probably among the oldest geological formations in existence anywhere. As he was untying his sneakers, he reached down and picked up a pebble that was almost a perfect tetrahedron. A moment later, he found another, and then another. It was amazing, he said, how often you came across this shape on the beach. Fuller took off his socks and then put his sneakers back on, and warned me to do the same; the tide was out, and the bottom would be strewn with sea urchins. His next bit of instruction concerned the art of swimming in Maine water. By going in and out very quickly several times, he said, and warming up between plunges, one could build up a tolerance to the cold. On our fourth entry, the crystalline water actually did seem a trifle less numbing, and I was prepared to believe that after a while it might become almost comfortable. Fuller warmed up between plunges by skipping stones on the water. He claimed he could skip any stone I found, whether it was flat or not, and he had no failures. Just as we were coming out of the water for the last time, a big seal surfaced near the rocky point some twenty yards away; he gave us a long, incredulous look and then vanished silently.


Suddenly noticing that I looked a little chilly—I had felt that it would somehow be in poor taste to get dressed before Fuller did, and while he was talking—he quickly put his clothes back on and then led the way to the house at a fast trot, pausing only to pick up an exceptionally good example of “our friend tetrahedron.” Fuller himself was not a bit cold.


Inboard N-form interplane struts held the upper plane high over the fuselage in place of a cabane. Outboard there was one more N-interplane strut between each wing, four in all. Ailerons were fitted on all three upper wings. The fourth wing, lowest of all, was quite different, much shorter in span. It was mounted independently of the other three, fixed to a dorsal keel extension and braced on each side with a V-strut from about mid-span to the root of the wing above. When the aircraft was parked, the wing was close to the ground and not far behind the undercarriage wheels.[1]


At 7:25 p.m. local time, the Hindenburg caught fire and quickly became engulfed in flames. Eyewitness statements disagree as to where the fire initially broke out; several witnesses on the port side saw yellow-red flames first jump forward of the top fin near the ventilation shaft of cells 4 and 5.[4] Other witnesses on the port side noted the fire actually began just ahead of the horizontal port fin, only then followed by flames in front of the upper fin. One, with views of the starboard side, saw flames beginning lower and farther aft, near cell 1 behind the rudders. Inside the airship, helmsman Helmut Lau, who was stationed in the lower fin, testified hearing a muffled detonation and looked up to see a bright reflection on the front bulkhead of gas cell 4, which "suddenly disappeared by the heat". As other gas cells started to catch fire, the fire spread more to the starboard side and the ship dropped rapidly. Although there were cameramen from four newsreel teams and at least one spectator known to be filming the landing, as well as numerous photographers at the scene, no known footage or photograph exists of the moment the fire started.



The description from 28th October 312, "A cross centered on the Sun" fits with modern-day photographs of Sun dogs.


I'm not that personally familiar with the recording quality of the H4N vs. the H2, but I would say this: while four channel ambience recordings can be useful, I know far more people who prefer to build their own surround (or the occassional quad for television) ambiences. You have more flexibility and control that way. Chances are good that if you record a quad ambience, and find material that is distracting or you don't like in one of the channels, you're going to break up that group and, in the very least, shift that channel...breaking up the strict quad interaction to anyways. You may replace that channel entirely.


Distribution lines use two systems, either grounded-wye ("Y" on electrical schematics) or delta (Greek letter "Δ" on electrical schematics). A delta system requires only a conductor for each of the three phases. A grounded-wye system requires a fourth conductor, the neutral, whose source is the center of the "Y" and is grounded. However, "spur lines" branching off the main line to provide power to side streets often carry only one or two phase wires, plus the neutral. A wide range of standard distribution voltages are used, from 2,400 V to 34,500 V. On poles near a service drop, there is a pole-mounted step-down transformer to provide the required mains voltage. In North America, service drops provide 240/120V split-phase power for residential and light commercial service, using cylindrical single-phase transformers. In Europe and most other countries, 230V three phase (230Y400) service drops are used. The transformer's primary is connected to the distribution line through protective devices called fuse cutouts. In the event of an overload, the fuse melts and the device pivots open to provide a visual indication of the problem. They can also be opened manually by linemen using a long insulated rod called a hot stick to disconnect the transformer from the line.


At electrical operated railways, pole routes were usually not built as too much jamming from the overhead wire would occur. To accomplish this, cables were separated using spars with insulators spaced along them; in general four insulators were used per spar. Only one such pole route still exists on the UK rail network, in the highlands of Scotland. There was also a long section in place between WymondhamNorfolk and Brandon in SuffolkUnited Kingdom; however, this was de-wired and removed during March 2009.


Three-phase systems may also have a fourth wire, particularly in low-voltage distribution. This is the neutral wire. The neutral allows three separate single-phase supplies to be provided at a constant voltage and is commonly used for supplying groups of domestic properties which are each single-phase loads. The connections are arranged so that, as far as possible in each group, equal power is drawn from each phase. Further up the distribution system, the currents are usually well balanced. Transformers may be wired in a way that they have a four-wire secondary but a three-wire primary while allowing unbalanced loads and the associated secondary-side neutral currents.


Three-wire and four-wire circuits[edit]


Wye (Y) and delta (Δ) circuits

There are two basic three-phase configurations: wye (Y) and delta (Δ). As shown in the diagram, a delta configuration requires only 3 wires for transmission but a wye (star) configuration may have a fourth wire. The fourth wire, if present, is provided as a neutral and is normally grounded. The "3-wire" and "4-wire" designations do not count the ground wire used above many transmission lines, which is solely for fault protection and does not carry current under non-fault conditions.

A four-wire system with symmetrical voltages between phase and neutral is obtained when the neutral is connected to the "common star point" of all supply windings. In such a system, all three phases will have the same magnitude of voltage relative to the neutral. Other non-symmetrical systems have been used.

The four-wire wye system is used when ground referenced voltages or the flexibility of more voltage selections are required. Faults on one phase to ground will cause a protection event (fuse or breaker open) locally and not involve other phases or other connected equipment.[citation needed] An example of application is local distribution in Europe (and elsewhere), where each customer may be only fed from one phase and the neutral (which is common to the three phases). When a group of customers sharing the neutral draw unequal phase currents, the common neutral wire carries the currents resulting from these imbalances. Electrical engineers try to design the system so the loads are balanced as much as possible within premises where 3-phase power is used.[12] These same principles apply to the wide scale distribution of power to individual premises. Hence, every effort is made by supply authorities to distribute all three phases over a large number of premises so that, on average, as nearly as possible a balanced load is seen at the point of supply.


In the very early days of commercial electric power, some installations used two-phase four-wire systems for motors. The chief advantage of these was that the winding configuration was the same as for a single-phase capacitor-start motor and, by using a four-wire system, conceptually the phases were independent and easy to analyse with mathematical tools available at the time.

3 phase power generating and delivering is more efficient than2 phase which in turn is more efficient than1 phase. Similarly, going up in the number of phases result in increased efficiency as well, i.e.4 phase is more efficient than3 phase and5 phase is more efficient than4 phase,...etc. The increase of efficiency as the number of phases increase is attributed to that power delivery becomes more continuous as the number of phases increases. A single phase (with resistive load) power delivery will have zero instantaneous power twice a cycle but no zero instantaneous power in the case of3 phase power and higher phases number with a more smooth power delivery as phases go up. It can be easily calculated to show that3 phase delivery is about150% more efficient than single phase. This is the optimum choice as going higher than that the increased efficiency does not justify the increased complexity of using more phases. I am not sure for the case of Aluminum melting industry which you say it uses48 phase for melting, I can only make an intelligent guess and let others judge it. Aluminum melting uses induction heating which involves high currents(powers). Hence it may be justified to increase the complexity and use a high number of phases in order to increase the efficiency of the melting process as possible. The complexity can be justified as control is probably using high power diodes and thyristors. It is not like in the case of power generation where having a3 phase generator/ motor is optimum and more than that means more brushes, 


Three-phase-to-four-phase transformer for four-phase power-transmission systems

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In this paper, a new three-phase-to-four-phase transformer with four-phase four-leg structure is first proposed, its electromagnetism principle is analyzed, and the properties and features of the transformer are also discussed. This transformer may be applicable to either four-phase transmission systems or autotransformer (AT) traction power-supply systems in electric railways.


Four Phase Power


The poles at the end of a straight section of utility line where the line ends or angles off in another direction are called dead-end poles in the United States. Elsewhere they may be referred to as anchor or termination poles. These must carry the lateral tension of the long straight sections of wire. They are usually made with heavier construction. The power lines are attached to the pole by horizontal strain insulators, either placed on crossarms (which are either doubled, tripled, or replaced with a steel crossarm, to provide more resistance to the tension forces) or attached directly to the pole itself.

Example of dead-end riser poles


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First we'll introduce the big four properties that come from the stress versus strain test. So now for the payoff of tensile testing. It turns out that there are four parameters in this overall plot that are routinely cataloged. And I'll make periodic references, and there's certainly references in the textbook to these data sources. For any engineering professional it's good to know about the ASM Handbook series. This is a multi volume source of information about a wide range of engineered materials. It historically has concentrated on structural metals, metallic materials, but has been broadened in recent decades to look at a full range of engineered materials, many non-metals included. But the first two volumes of this more than 20 volume series concentrates on basically cataloging the properties, the characteristics of metal alloys, both ferrous and non-ferrous, both iron-containing and non-iron-containing. And you'll see that the four parameters that are cataloged over and over again, tend to be four that come directly from the tensile test. We've already been talking about this initial slope. That is distinctive, linear. We refer to this as the modulus of elasticity. And again, we will be re-emphasizing along the way how this associated with the strength of the atomic bombs and the crystalline structure of the metal alloy. The yield strength we’ve already defined. The tensile strength, parameter three, is simply that maximum stress demonstrated by the material in its overall path to destruction as it's taken to failure. And then, finally, the ductility, or the deformability, kind of a sense of the overall extent of deformation of the material. And that's this item down here after the elastic recovery. Once the item is broken, we also get that elastic snap back, as the load is removed. And one ends up then with a final length, which corresponds to the extent of the overall plastic deformation. So those four properties are going to be the ones we'll see, that most of the common structural metals that are available to us will have this information. And it will tend to be systematically collected in a source such as the ASM Handbook, an especially comprehensive source being that set of volumes.