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Three geometries – Euclidean, Hyperbolic, Elliptical

Three geometries - Euclidean, Hyperbolic, Elliptical
Three geometries – Euclidean, Hyperbolic, Elliptical

There are precisely three different classes of three-dimensional constant-curvature geometry: Euclidean, hyperbolic and elliptic geometry. The three geometries are all built on the same first four axioms, but each has a unique version of the fifth axiom, also known as the parallel postulate. The 1868 Essay on an Interpretation of Non-Euclidean Geometry by Eugenio Beltrami (1835 – 1900) proved the logical consistency of the two Non-Euclidean geometries, hyperbolic and elliptical.

The parallel postulate is as follows for the corresponding geometries.

Euclidean geometry: Playfair’s version: “Given a line l and a point P not on l, there exists a unique line m through P that is parallel to l.” Euclid’s version: “Suppose that a line l meets two other lines m and nso that the sum of the interior angles on one side of lis less than 180°. Then m and n intersect in a point on that side of l.” These two versions are equivalent; though Playfair’s may be easier to conceive, Euclid’s is often useful for proofs.

Hyperbolic geometry: Given an arbitrary infinite line l and any point P not on l, there exist two or more distinct lines which pass through P and are parallel to l.

Elliptic geometry: Given an arbitrary infinite line land any point P not on l, there does not exist a line which passes through P and is parallel to l.

Source and more info: https://en.m.wikibooks.org/wiki/Geometry/Hyperbolic_and_Elliptic_Geometry

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Trifid Nebula

Trifid Nebula

In the Center of the Trifid Nebula Image Credit: Subaru Telescope (NAOJ), Hubble Space Telescope, Martin Pugh; Processing: Robert Gendler

What’s happening at the center of the Trifid Nebula? Three prominent dust lanes that give the Trifid its name all come together. Mountains of opaque dust appear near the bottom, while other dark filaments of dust are visible threaded throughout the nebula. A single massive star visible near the center causes much of the Trifid’s glow. The Trifid, cataloged as M20, is only about 300,000 years old, making it among the youngest emission nebulas known. The star forming nebula lies about 9,000 light years away toward the constellation of the Archer (Sagittarius). The region pictured here spans about 10 light years. The featured image is a composite with luminance taken from an image by the 8.2-m ground-based Subaru Telescope, detail provided by the 2.4-m orbiting Hubble Space Telescope, color data provided by Martin Pugh and image

Trifid Nebula
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The comet, the whale and the hockey stick

Comet, whale, hockey stick

The Comet, the Whale, and the Hockey Stick

Image Credit & Copyright: Grand Mesa Observatory, Terry Hancock / Tom

Masterson

Closest to the Sun on March 1, and closest to planet Earth on April 23, this Comet ATLAS (C/2020 R4) shows a faint greenish coma and short tail in this pretty, telescopic field of view. Captured at its position on May 5, the comet was within the boundaries of northern constellation Canes Venatici (the Hunting Dogs), and near the line-of-sight to intriguing background galaxies popularly known as the Whale and the Hockey Stick. Cetacean in appearance but Milky Way sized, NGC 4631 is a spiral galaxy seen edge-on at the top right, some 25 million light-years away. NGC 4656/7 sports the bent-stick shape of interacting galaxies below and left of NGC 4631.

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Physics has a law that explains everything. And it’s brought to you by the number three

Jamie Seidel: News Corp Australia Network

The rule of three has become something akin to a social law of gravity — as if the number is behind everything.

Three groups of experimentalists have independently observed a strange state of matter that forms from three particles of any type and at any scale, from practically infinitesimal to infinite.

Forget pairs. They’re old pat. And 42? We still don’t know the question.

Three rings to rule them all, and in the darkness bind them ... apologies  Lord Of The Rings purists.
Three rings to rule them all, and in the darkness bind them … apologies to Lord Of The Rings purists.

Comedians insist three is the best pattern to exploit perceptions and deliver punchlines; three features prominently in titles, such as The Three Little Pigs, Three Musketeers, Goldilocks and the Three Bears; even the Romans believed three was the ultimate number: “Omne trium perfectum” was their mantra — everything that comes in threes is perfect.

Now, it seems Mother Nature may also think in threes. Especially at the very edge of physics — quantum mechanics.

A Soviet nuclear physicist first proposed the idea back in the 1970s — and was met with derision.

For 45 years number-crunchers around the world have been attempting to topple Vitaly Efimov’s idea and prove his equations wrong.

Shih-Kuang Tung of the University of Chicago
Shih-Kuang Tung of the University of Chicago holding Borromean rings, which have often been used as a symbol of unity. If one ring is removed, all three fall apart.

They’ve failed; and his “outlandish” theory is now on the point of being proven.

Most importantly, Efimov felt that sets of three particles could arrange themselves in an infinite, layered pattern. What form these layers take helps determine the makeup of matter itself.

Jump forward four decades, and technological advances now allow his groups of three quantum particles to be studied and manipulated.

The quantum condition — now known as Efimov’s state — is visible only under supremely cold conditions. Matter, when chilled to a few billionths of a degree above Absolute Zero, does strange things …

If you want the technical details, read Quanta Magazine’s article which examines the recent research papers.

Continue reading Physics has a law that explains everything. And it’s brought to you by the number three
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These Three Things Need to Happen Before Stocks Bottom Out, Credit Suisse Says

By Callum KeownUpdated March 16, 2020 10:29 am ET / Original March 16, 2020 9:58 am ET

When will stocks reach the low and what will the recovery look like?

Workers wearing protective gear in South Korea.ASSOCIATED PRESS
Workers wearing protective gear in South Korea.ASSOCIATED PRESS

Credit Suisse said it needed to see three conditions required for a trough in global stocks:

1. Clear-cut fiscal easing in the U.S. — which happened late on Sunday;

2. A peak in daily infection rates

3. A trough in global purchasing managers indexes, which it said could happen in May.

In the severe acute respiratory syndrome crisis, markets bottomed out a week daily new infections hit a peak, the bank’s research analysts said.

“We expect a V-shaped recovery ultimately and would be buyers of equities on a one-year view; we believe markets will rise 15-20% over the next 12 months. 

“Historically when we look at exogenous supply-side shocks, markets tend to rise very rapidly from the trough (SARS, Kobe earthquake, Suez, 1987),” they said.

The analysts, led by Andrew Garthwaite, favored stocks in Asia (a commodity-importing region on top of the virus) relative to Europe. In a new realistic worst-case scenario, U.S. earnings would drop 20% and the S&P 500 would fall to 2,200 points, they added.

They also expected “massive” monetary and fiscal stimulus. “This should enable a V-shaped recovery that by the end of 2021 could make up for much of 2020’s lost growth,” they said.

Source: https://www.barrons.com/articles/these-three-things-need-to-happen-before-stocks-bottom-out-credit-suisse-says-51584367103

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Coronavirus can stay infectious for 3 days on surfaces. But it’s still okay to check your mail.

March 13, 2020 at 8:00 AM EDT

Excerpt: Scientists studying the novel coronavirus are quickly uncovering features that allow it to infect and sicken human beings. Every virus has a signature way of interacting with the world, and this one — SARS-CoV-2, which causes the disease covid-19 — is well-equipped to create a historic pandemic.

Corona virus covid-19
Corona virus covid-19

The coronavirus may take many days — up to 14 — before an infection flares into symptoms, and although most people recover without a serious illness, this is not a bug that comes and goes quickly. A serious case of covid-19 can last for weeks.

This coronavirus can establish itself in the upper respiratory tract, said Vincent Munster, chief of the Virus Ecology Section of Rocky Mountain Laboratories, a facility in Hamilton, Mont., that is part of the National Institute of Allergy and Infectious Diseases. That enables the virus to spread more easily through coughing and sneezing. Munster and his colleagues have been studying the novel coronavirus under laboratory conditions to better understand its viability outside a host organism — in the air and on surfaces.

Those experiments found that at least some coronavirus can potentially remain viable — capable of infecting a person — for up to 24 hours on cardboard and up to three days on plastic and stainless steel.

Source and to read more: The Washington Post at https://www.washingtonpost.com/health/coronavirus-can-stay-infectious-for-days-on-surfaces/2020/03/12/9b54a99e-6472-11ea-845d-e35b0234b136_story.html


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Voxel

Voxel
Voxel – Wikipedia

A three dimensional pixel. A hologram compresses 3D information onto a 2D representation. Two different representations of reality. The world is a pixelated world, not a voxelated world. It’s a hologram.

We know our cosmic horizon of the observable universe is at least 1/1000th in volume of the size of the known universe through observation.

In his words, The universe is at least 1000 times larger in volume than the region what we can ever see. The rest is beyond our horizon. This is like an event horizon of a black hole, but it is a cosmic horizon.

What is the meaning of the stuff we can never detect?

How can we confirm it by real observation?

What is the proper description of a world that is bigger than the cosmic horizon? 

Is our cosmic horizon a two-dimensional scrambled hologram of all that lies beyond it?

Leonard Susskind
Leonard Susskind

Leonard Susskind on The World As Hologram.

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Rule of Thirds – Top 5 Tips for Photographers

What differentiates an amateur photographer and a professional is not the mastery of technical details. A good photographer knows how to compose an image well. There are many rules of composition; we will study one of the most commonly used ones. And that composition rule is called the rule of thirds.

Rule of Thirds

The rule of thirds means that you have to place your subject at any one-third of the image frame. Most of the cameras these days have an option to display various types of grids. The grid that is the most common is the 3*3 grid. So, the points where the lines meet is the point where your subjects should be placed. You would have to consider other factors along with it. Placing an image randomly on any of the points will not make an image great. Give it some thought on which point would make the most sense.

Here are some tips for you to learn and master this rule.

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Big Oh(O) Big Theta(Θ) Big Omega(Ω)

big O Notation

Analysis of Algorithms

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. It is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation.

Big Oh Running Time Complexity
Big Oh Running Time Complexity

Two simple concepts separate properties of an algorithm itself from properties of a particular computer, operating system, programming language, and compiler used for its implementation. The concepts, briefly outlined earlier, are as follows:

The input data size, or the number n of individual data items in a single data instance to be processed when solving a given problem. Obviously, how to measure the data size depends on the problem: n means the number of items to sort (in sorting applications), number of nodes (vertices) or arcs (edges) in graph algorithms, number of picture elements (pixels) in image processing, length of a character string in text processing, and so on.

The number of elementary operations taken by a particular algorithm, or its running time. We assume it is a function f(n) of the input data size n. The function depends on the elementary operations chosen to build the algorithm.

Algorithms are analyzed under the following assumption: if the running time of an algorithm as a function of n differs only by a constant factor from the running time for another algorithm, then the two algorithms have essentially the same time complexity. Functions that measure running time, T(n), have nonnegative values
because time is nonnegative, T(n) ≥ 0. The integer argument n (data size) is also nonnegative.

Definition 1 (Big Oh)

Big Oh Rank Meaning
Big Oh Rank Meaning

Let f(n) and g(n) be nonnegative-valued functions defined on nonnegative integers n. Then g(n)is O(f(n)) (read “g(n)is Big Oh of f(n)”) iff there exists a positive real constant c and a positive integer n0 such that g(n) ≤ c f(n) for all n > n0.

Note. We use the notation “iff ” as an abbreviation of “if and only if”.

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QPR – Three Steps Anyone Can Take to Save a Life

What is QPR?

QPR logo
QPR

QPR stands for Question, Persuade and Refer — three simple steps anyone can learn to help save a life from suicide.

Our Mission

To save lives and reduce suicidal behaviors by providing innovative, practical and proven suicide prevention training. We believe that quality education empowers all people, regardless of their background, to make a positive difference in the life of someone they know.

What does QPR mean?

QPR stands for Question, Persuade, and Refer — the 3 simple steps anyone can learn to help save a life from suicide.

Just as people trained in CPR and the Heimlich Maneuver help save thousands of lives each year, people trained in QPR learn how to recognize the warning signs of a suicide crisis and how to question, persuade, and refer someone to help. Each year thousands of Americans, like you, are saying “Yes” to saving the life of a friend, colleague, sibling, or neighbor.

QPR can be learned in our Gatekeeper course in as little as one hour.

What is a Gatekeeper?

According to the Surgeon General’s National Strategy for Suicide Prevention (2001), a gatekeeper is someone in a position to recognize a crisis and the warning signs that someone may be contemplating suicide.

Gatekeepers can be anyone, but include parents, friends, neighbors, teachers, ministers, doctors, nurses, office supervisors, squad leaders, foremen, police officers, advisors, caseworkers, firefighters, and many others who are strategically positioned to recognize and refer someone at risk of suicide.

Read more-Partial Source: https://qprinstitute.com/about-qpr

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NPK Ratio

flower garden

The N-P-K ratio is the percentage by volume of nitrogen (chemical symbol N), phosphorus (P), and potassium (K) in fertilizer. A 16-16-16 fertilizer, for example, contains 16% nitrogen, 16% phosphorus, and 16% potassium.

NPK ratio
NPK ratio

How is NPK Calculated?

To calculate the pounds of nitrogen in a bag of fertilizer, multiply the weight of the bag by the percent nitrogen (this is the first number in the N-P-K designation on the front of the bag). Then divide the pounds of nitrogen by the area the bag states it will cover to get the pounds of nitrogen per 1,000 sq. ft.

Roles of NPK

The first number of the ratio indicates the amount of nitrogen in the fertilizer. Nitrogen serves a few different roles but its primary benefit to grass is to help produce lush, green leaves. The second element is phosphorus, which is focused on more of the downward growth and fuels important developments such as root growth. The final nutrient represented in the ratio is potassium. This particular nutrient focuses more on resistance. If you already have an established lawn that’s starting to suffer from stress or diseases then the application of potassium is crucial to the health of the grass.

n-p-k
n-p-k

What’s the Best Ratio?

The NPK ratio represents is the percentage of nitrogen (N), phosphorus (P), and potassium (K) in the fertilizer. So how do you what’s best for what ratio? Here are some basic rules to follow. If you are starting a new lawn then get lawn fertilizer that has a higher percentage of phosphorus and potassium. At this stage, it’s important to focus on root development and disease resistance.

If you are installing a new layer of sod then apply a similar ratio to what you would use for new lawns. Although new sod does have established grass, the roots themselves have been shaved off so it is vital to up the amount of phosphorus in the soil for root development purposes.

Finally, if you are well into the gardening season and have an established lawn then focus on using a fertilizer that has a higher composition of nitrogen. Before Using Lawn Fertilizer perform a test to determine the amount of nutrients that already exist in the soil. This can be done on your own through the use of NPK soil test kit.

Partial Source: http://www.jgilorganic.com/npk-lawn-care/

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Three ways to insert CSS – cascading style sheets

cascading style sheets

CSS How To…


When a browser reads a style sheet, it will format the HTML document according to the information in the style sheet.

working with CSS
working with CSS

Three Ways to Insert CSS

There are three ways of inserting a style sheet:

  • External style sheet
  • Internal style sheet
  • Inline style

External Style Sheet

With an external style sheet, you can change the look of an entire website by changing just one file!

Each page must include a reference to the external style sheet file inside the <link> element. The <link> element goes inside the <head> section:

Example

<head>
<link rel="stylesheet" type="text/css" href="mystyle.css">
</head>
Try it Yourself »

An external style sheet can be written in any text editor. The file should not contain any html tags. The style sheet file must be saved with a .css extension.

Here is how the “mystyle.css” looks:

body {
  background-color: lightblue;
}

h1 {
  color: navy;
  margin-left: 20px;
}

Note: Do not add a space between the property value and the unit (such as margin-left: 20 px;). The correct way is: margin-left: 20px;


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