⨀⨀⨀ Margaret Thatcher ⪢⪢
#people
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◎◎◎ complement ⪢⪢
When two angles are complementary, we say that one angle is the complement of the other. #math
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◎◎◎ invertebrate ⪢⪢
Invertebrates are animals that do not have backbones. → vertebrate
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◎◎◎ vertebrate ⪢⪢
Vertebrates are animals that have spines or backbones.
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◎◎◎ malvertising ⪢⪢
Malverting is the word for online ads that can attack your computer if you click on them. #bookmark
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◎◎◎ mandatory ⪢⪢
Mandatory is something that must be done or is required by law.
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◎◎◎ riot ⪢⪢
A riot is a crowd that reacts to bad news by violently breaking laws.
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◎◎◎ myth ⪢⪢
A myth is a traditional story that explains a culture's history and beliefs. #bookmark
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◎◎◎ lid ⪢⪢
A lid is a top for a box or container that can be removed. #grammar #bookmark
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◎◎◎ subject ⪢⪢
a topic that is being discussed or taught
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◎◎◎ offense ⪢⪢
An offense is an action that breaks the law and requires punishment.
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◎◎◎ habitual ⪢⪢
If something is habitual, it is a behavior that a person usually does or has. → habit
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◎◎◎ innovation ⪢⪢
An innovation is a product or idea that is new or very original.
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◎◎◎ mob ⪢⪢
A mob is a large crowd of people that often wants to cause violence.
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◎◎◎ certify ⪢⪢
To certify something means to confirm that its results are true.
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◎◎◎ pest ⪢⪢
A pest is an animal or insect that hurts plants or food.
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◎◎◎ mash ⪢⪢
To mash something is to crush it so that it is soft.
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◎◎◎ arrogant ⪢⪢
If someone is arrogant, they think that they are more important than others.
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◎◎◎ imprint ⪢⪢
An imprint is an effect or lesson from an experience that is hard to forget. #bookmark
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◎◎◎ complex number ⪢⪢
A complex number is a number that can be expressed in the form a + bi where a and b are real numbers and i is the square root of -1. #math
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◎◎◎ muscle ⪢⪢
Muscle is a mass of tissue attached to bone that helps you move.
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◎◎◎ prime number ⪢⪢
A _____ is one that's only divisible by itself and 1.
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◎◎◎ coronavirus ⪢⪢
Coronaviruses are a large group of viruses. They consist of a core of genetic material surrounded by an envelope with protein spikes. This gives it the appearance of a crown. 'Crown' in Latin is called 'corona' and that's how these viruses get their name.
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 that ⪢⪢
But then they decided that what was the best was to build a hidden trapdoor. #fairy
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 that ⪢⪢
And nobody in the inn knew that he was the pirate black dog. #bookmark
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 that ⪢⪢
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 1646 - 1716 Gottfried Wilhelm Leibniz
Leibniz did similar work just a few years later, independently of Newton, and it is actually his notation that we still use today.
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◌◌◌ Point
First we look at a point. This is nothing more than a location in space. It is zero-dimensional, meaning that it has no dimensions of any kind.
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 1643 - 1727 Isaac Newton
Galileo had already discovered some years prior that the distance traveled by a falling object is represented by a function of time. Newton wondered how one could calculate the velocity of the object at any particular instance during the fall.
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 07 How to organize, add and multiply matrices
By now, I'm sure that in just anything you do in your life, you need numbers. In particular, though some fields don't just need a few numbers, they need lots of them. How do you keep track of those numbers?
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◌◌◌ Point
We represent points with little dots and some capital letter, making sure to realize that the dot we draw is infinitely larger than the point it is meant to represent.
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○○○ pneumonia ⪢⪢
In December 2019, there was a cluster of pneumonia cases in China. Investigations found that it was caused by a previously unknown virus, now named the 2019 Novel Coronavirus.
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 past of will
He said that Tom would have to use the treasure to do the devil's work.
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 BC 0500? Hippasus
According to Pythagoras theorem the diagonal length of a square with each side measuring one unit would be square root of two. The assumption that square root of two could be expressed as a ratio of two integers deduces a contradiction.
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 03 Rates of Change
Galileo had already discovered some years prior that the distance traveled by a falling object is represented by a function of time. Newton wondered how one could calculate the velocity of the object at any particular instance during the fall.
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 Logarithms Explained
In the same way that division is the inverse of multiplication a logarithm is just the inverse of exponentiation.
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 Change of base
Log base b of n. What power should I put in the exponent of b so b to that power will give me n.
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◌◌◌ Indians
When the first Europeans came to North America, they mistakenly believed that they had reached India, so they referred to the people as Indians. #Level 3
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  Darwin
Individuals that lacked those characteristics would become more likely to die without reproducing. #listening
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○○○ Somewhere beyond the sea, ⪢⪢
somewhere waiting for me, my lover stands on golden sands and watches the ships that go sailing. Somewhere beyond the sea, she's there watching for me. If I could fly like birds on high, then, straight to her arms, I'd go sailing. #song
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○○○ I'm sailing away, ⪢⪢
set an open course for the virgin seas. I've got to be free, free to face the life that's ahead of me. On board I'm the captain so climb aboard. We'll search for tomorrow on every shore. And I'll try, oh Lord, I'll try to carry on. #have_got #song
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○○○ would ⪢⪢
His heart _____ soften when he saw Persephone and he was amazed by her youth and her beauty and her freshness. He asked Demeter to marry Persephone but Demeter said that that _____ never happen.
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○○○ spillover ⪢⪢
It's known that coronaviruses circulate in a range of animals. Sometimes these viruses can make the jump from animals to humans. This is called a spillover. → spill
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◌◌◌ Roraima
10 Real Places On Earth That Seem Scientifically Impossible
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◌◌◌ Bitcoin
The online magazine wired.com reported that the bitcoin was worth about 434 dollars as of January 6. The company Juniper Research says there were 1.3 million users in 2015. It estimates there will be 4.3 million users by the end of the next year.
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 the bridge riddle - Alex Gendler
Taking that internship in a remote mountain lab might not have been the best idea. Pulling that lever with the skull symbol just to see what it did probably wasn’t so smart either.
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 BC 0300? Euclid
It was the Greek mathematician Euclid who produced the first precise description of the golden section. A length is devided into two parts in such a way that the smaller part is to the larger part in the same proportion as the larger one is to the whole.
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 1571 - 1630 Johannes Kepler
Keplar observed that the relationship between a number in Fibonacci sequence and the previous number more and more closely approaches the irrational number Φ the longer the sequence is continued and Φ describes nothing other than the golden section.
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 41 Logarithms Part 1
When we say log base b of x equals y, we are saying b to the y equals x. With logs, the base of the log raised to the power of what's on the other side of the equal sign will equal the number that the log is operating on.
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○○○ case ⪢⪢
South Korea now has over 200 reported cases of the new coronavirus. That is 4 times the number on Tuesday. 2020-02-21
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  Companies That Didn’t Exist 10 Years Ago
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◌◌◌ Hippasus
According to Pythagoras theorem the diagonal length of a square with each side measuring one unit would be square root of two. The assumption that square root of two could be expressed as a ratio of two integers deduces a contradiction.
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 Kim Jung-un
Kim Jung-un's abusive use of missiles and his nuclear threats show that he is begging for war. War is never something the United States wants. We don't want it now. But our country's patience is not unlimited.
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 The Poincare Conjecture
In the early 1900s mathematicians and physicists were very interested in the shape of space. New experiments and theories were being developed that would ultimately create relativity theory and change our entire view of the universe.
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○○○ will ⪢⪢
My wish is that your son _ be the most handsom of all men. #will_would
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○○○ was to ⪢⪢
Ashamed he decreed that the prince was use a special hat that would cover his ears and that he was never to take it off. The prince was not to know about his donkey ears. → decree #be
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○○○ get ⪢⪢
Social media is not real. You're only seeing the curated part of someone's life. Your life is different from theirs because you get to experience the stuff that never gets posted. → curate #quote
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○○○ Copernicus's theory ⪢⪢
When Galileo announced that he believed in Copernicus's theory that the earth revolved around the sun, some officials of the Roman Catholic church were angry. #possessive
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○○○ I look to the sea. ⪢⪢
Reflections in the waves spark my memories, some happy some sad. I think of childhood friends and the dreams we had. We live happily forever so the story goes. But somehow we missed out on the pot of gold. And we'll try best that we can to carry on. #song
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○○○ espouse ⪢⪢
Militant Islamic terrorists in Egypt have left a bloody trail of destruction. The loss of inocent lives from deadly bombings and other attacks had led the government to condemn extremist Islamic terrorists that espouse violence.
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○○○ would ⪢⪢
Meantime he plays the piano for a world that now realizes you can discover stunning talent in people you'd never expect.
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○○○ acrobat ⪢⪢
There were acrobats at the circus that did impressive and complicated jumps. #bookmark
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○○○ blindfold ⪢⪢
That night, the captain of the thieves took the blindfolded carpenter a second time. #fairy
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○○○ black box ⪢⪢
In China, officials say they have recovered the "black box" flight recorder of the China Eastern Airplane that crashed days ago, killing 132 people. 2022-03-23
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○○○ Solomon Islands ⪢⪢
China confirms it signed a security agreement with the Solomon Islands that could send Chinese police and armed forces to the Pacific nation. 2022-04-20 #image #place
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○○○ 2022-10-10 ⪢⪢
On national day in Taiwan, President Tsai Ing-wen warns China that the island would never give up its democratic way of life.
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○○○ fan ⪢⪢
Indonesia's security minister promises an investigation into a stampede that killed 125 soccer fans who were crushed Saturday in Malang, Java. 2022-10-03
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 01 Hippasus
○ According to Pythagoras theorem the diagonal length of a square with each side measuring one unit would be square root of two. ○ The assumption that square root of two could be expressed as a ratio of two integers deduces a contradiction.
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○○○ ingrain ⪢⪢
Since ancient times the belief that stars could influence the way we live was already ingrained. #pillow
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○○○ Self Determination ⪢⪢
The idea that nations should have the right to govern themselves without interference from other countries.
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○○○ cosmology ⪢⪢
And part of this belief was that everything from cosmology and metaphysics to music and morals followed eternal rules describable as ratios of numbers.
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○○○ luxury ⪢⪢
That's a luxury that most people in the world don't have today.
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○○○ logarithm ⪢⪢
x⍻b = y With logs, the base of the log raised to the power of what's on the other side of the equal sign will equal the number that the log is operating on. #math
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○○○ Orion ⪢⪢
If you can find _____ , you can find every other constallation that surrounds it within the winter sky.
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○○○ synchronous ⪢⪢
Because the moon's period of rotation is equal to its period of revolution, that is to say, because the moon takes the same amount of time to spin as it does to orbit the earth, we from the earth only ever see one face of the moon.
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○○○ miller ⪢⪢
And although my eyes were open. They might have just as well been closed. And so it was that later. As the _____ told his tale. That her face, at first just ghostly. Turned a whiter shade of pale. #song
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○○○ proof ⪢⪢
Gave _____ through the night that our flag was still there #song
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○○○ spangle ⪢⪢
Oh, say does that star-spangled banner yet wave #song
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○○○ off ⪢⪢
We couldn't cut the fat off four whales in one day so we had to watch them that night. #pillow
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○○○ predominate ⪢⪢
The astrological horoscope that predominates in the West has its origins in several cultures. #pillow
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○○○ Ahab ⪢⪢
He had a hard face with lines on it from years of sun and wind. An ugly white line ran down from the top of his head. Did it go down to his feet? Who or what did that to him? What fight did he lose so badly? #pillow
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○○○ Starbuck ⪢⪢
Starbuck was a young man. When you saw his black clothes and sad face, you could forget that.
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○○○ topology ⪢⪢
Topology is a branch of math, which is kind of like geometry. It studies shapes and spaces, but ones that are arbitrarily stretchy and bendy. It's sometimes called rubber sheet geometry.
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○○○ Ben Zimmer ⪢⪢
Ben Zimmer writes about language for the Wall Street Journal. He says, "There has been a lot of debate recently about something that has been in our language for centuries."
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○○○ third person ⪢⪢
He explains that English does not have a third person singular pronoun that does not identify as male or female. Zimmer says that more and more "they" is being used to replace the traditional phrase, "he or she".
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○○○ Anna Matteo ⪢⪢
Metcalf says the decision for the word of the year is not based on science. Instead, he says the A.D.S. chooses from words that express the concerns and stories of the past year. For VOA Learning English, I'm Anna Matteo.
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○○○ ahead ⪢⪢
Our first discovery is one that archeologists know the function of but we can't imagine how the Roman's were able to come up with something so many centuries ahead of its time.
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 01 The Greeks, Newton and Leibniz
Whether differential or integral both concepts involve the idea that we can do something infinately many times and get a finite answer that is useful.
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 Φ ≈ 1.618
Keplar observed that the relationship between a number in Fibonacci sequence and the previous number more and more closely approaches the irrational number Φ the longer the sequence is continued and Φ describes nothing other than the golden section. #math
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○○○ Golden Section ⪢⪢
It was the Greek mathematician Euclid who produced the first precise description of the golden section. A length is devided into two parts in such a way that the smaller part is to the larger part in the same proportion as the larger one is to the whole.
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 √2 ≈ 1.414
According to Pythagoras theorem the diagonal length of a square with each side measuring one unit would be square root of two. The assumption that square root of two could be expressed as a ratio of two integers deduces a contradiction. #math
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 That & Which
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 Logarithms Explained
What is the power that I should raise this base to in order to get this number?
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 Logarithms Explained
Anytime you see log base b of some number n, you can think about it as asking the question "What power do I need to put in my exponent to get b to that power equal to this number n?"
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○○○ flag ⪢⪢
Gave proof through the night that our _____ was still there #song
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○○○ banner ⪢⪢
Oh, say does that star-spangled _____ yet wave #song
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○○○ unto ⪢⪢
Do unto others what you would have them do unto you. ┆ You would have others do that unto you if you could. → onto #quote #conditional ▲→▲ #bookmark
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○○○ If you've been following me for a while, ⪢⪢
you know that I often talk about the importance of consistent repetitive active practice because that leads to muscle memory or automaticity, the ability to do something without thinking about it too much or stressing about it.
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○○○ sight ⪢⪢
No doubt he would have thought that he had caught sight of two winged gods. ┆ If a fisherman or a shepherd had looked up just then, he would have thought that he had caught sight of two winged gods. #conditional ◁→◁
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○○○ mortal ⪢⪢
Who could have believed that a mortal father and son had mastered the art of flight? ┆ Who could have believed that a mortal father and son had mastered the art of flight if anyone had looked up just then? #conditional ◁→◁
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