What Does Pi Mean In Mathematics
The mathematical pi is defined as the ratio of the circumference of a circle to its diameter. Its also known as Archimedes Constant, after the ancient Greek mathematician of the same name, who, in addition to coming up with an algorithm for calculating pi, also invented an early type of irrigation pump called the Archimedian screw. Very medieval-sounding, but we digress.
What makes pi so magical is that it doesnt matter how big or small the circle may be: the pi ratio remains the same.
Pi is whats known as an irrational number, which means, in part, that it can never terminate or repeat when written out in form. As far as we can tell, it goes on forever, which is a bit mind-boggling. Computers have calculated pi to decimal places in the trillions.
It is also a transcendentalnumber, a concept that exceeds the scope of this post but is interesting in and of itself.
From Zero To Mathematical Hero
As mathematical concepts developed, zero eventually crept out of India and began to stretch across the globe. Around 1200 A.D., famed Italian mathematician Fibonacci returned to the Western world after a childhood spent in what is now Algeria. There, he was educated by a Moorish teacher, and was introduced to the world of Arabic numerals. When he returned to Europe, he brought nothing with himthe concept of nothing, that is.
That didnt sit so well back home. Zero landed in Europe during the era of the Crusades, and people were skeptical of Arab ideas. The whole concept of nothing actually was quite a difficult idea for a lot of people, especially Christians, says mathematician Hannah Fry. Their idea was sort of eternity and theres no beginning and no end of God. So the very concept of nothingness made them feel quite uncomfortable.
In addition to philosophical qualms, zero presented some cause for consternation among the money-minded. In the 13th century, the city of Florence, Italy banned zero and all other Arabic numerals, claiming that the circle shape could be easily doctored into a 6 or a 9 by an enterprising merchant, and could be a gateway to negative numbersand the dreaded concept of debt and moneylending.
What Is The Origin In Math Definition And Illustration
In the coordinate system, the origin is the point at which the x-axis and the y-axis intersect.
In the figure above, the origin is shown with the green dot. The ordered pair for the origin is and as you can see, the x-coordinate of the origin is 0 and the y-coordinate of the origin is 0.
What is a vector? Definition, explanations and easy to understand read life examples.
What are vertical angles? Definition, explanation and easy to understand examples.
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What is a vector? Definition, explanations and easy to understand read life examples.
What are vertical angles? Definition, explanation and easy to understand examples.
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Uses And Meaning Of The Sigma Symbol Throughout History
Historians believe that the word sigma comes from the Greek word sig-jo which literally translates to I hiss.
The sigma symbol has been held in high importance since ancient times. In Ancient Greece, the sigma symbol was printed on coins. It was also used in architecture, and was displayed prominently in churches.
Moreover, the sigma sign has been of decorative value as well. A 6th Century mosaic work in the Byzantine church of St. George in Jordan features the sigma sign on the famous Madaba Map.
In the modern-day world, the sigma sign is renowned for its use in mathematical formulas. In the field of math, the word sigma either means summation or standard deviation.
This is because the uppercase sigma is used as a summation sign in mathematics, whereas the lowercase sigma refers to the square root of variance, or in simple words, the standard deviation.
The two sigma symbols have their own distinct formulas. An example of sigma as a summation operator is given below.
Princeton’s Wordnetrate This Definition:
beginning, origin, root, rootage, sourcenoun
the place where something begins, where it springs into being
“the Italian beginning of the Renaissance” “Jupiter was the origin of the radiation” “Pittsburgh is the source of the Ohio River” “communism’s Russian root”
origin, descent, extractionnoun
properties attributable to your ancestry
“he comes from good origins”
origin, origination, inceptionnoun
an event that is a beginning a first part or stage of subsequent events
the point of intersection of coordinate axes where the values of the coordinates are all zero
the source of something’s existence or from which it derives or is derived
“the rumor had its origin in idle gossip” “vegetable origins” “mineral origin” “origin in sensation”
lineage, line, line of descent, descent, bloodline, blood line, blood, pedigree, ancestry, origin, parentage, stemma, stocknoun
the descendants of one individual
“his entire lineage has been warriors”
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What Is The Origin Of The Word Rational
According to Etymonline, the word rational has been used since the late c14 as the Middle English racional. This word has been used since mid-c15 to describe people. This word comes from the Old French racional, Old French rationel and Old French racionel meaning pontifical stole, a pallium, an ornament, the neuter of Latin rationalis/Latin ratinlis, from the Latin ratio/rati, the genitive rationis meaning a reckoning or reason. These are also seen in the first etymology of the Medieval Latin rationale. This has been used in the field of mathematics since the 1560s. One can add the suffixes ly, ity, ise, e, ist, and the prefix ir to form the related words irrational , ratio , ration , rationale , rationalist , rationality , rationally and rationalize .
How To Find The Range Between Two Numbers
The range is typically used to find the dispersion of values in a data set comprising several values. However, you dont need all the other numbers to find the range between two numbers.
Finding the range between two numbers is the same as finding the range of a set of data.
Here you have a set of numbers:
To find the range, you take the greatest value, 10
Now, what if you have only the two numbers 10
The range between these two numbers is the same, 10
Finding the range of a data set is the same as finding the range between two numbers.
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Origin Of The Sigma Symbol
Some semioticians suggest that the sigma symbol is derived from shin.
Shin is the twenty-first character in the Phoenician alphabet, sometimes also referred to as the Proto-Canaanite alphabet. In case you are unaware, Phoenician is the oldest known system of alphabets that dates as far back as 1050 BC. It is believed that the ancient civilizations in what constitutes modern day Lebanon, Syria and northern Israel heavily relied on this system of alphabets for communication.
The Phoenician shin looks exactly like the capital letter W in the modern English alphabet. Rotate it 90 degrees clockwise and you get the capital version of the sigma symbol.
Using Range In Real Life
Range is used in real life to make mathematical calculations. Range can be used to calculate the amount of time that has passed, like when calculating your age.
The current year is , and you were born in 2005 . How old are you? Or how much time has passed?
years have passed, so if your 2020 birthday has already passed, then you are 15 years old.
Range is also used in real life to figure out the dispersion of a high school class’ test scores, to determine the price range for a service, and much more.
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Coordinate System And Ordered Pairs
A coordinate system is a two-dimensional number line, for example, two perpendicular number lines or axes.
This is a typical coordinate system:
The horizontal axis is called the x-axis and the vertical axis is called the y-axis
The center of the coordinate system is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are .
An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of . The first number corresponds to the x-coordinate and the second to the y-coordinate.
To graph a point, you draw a dot at the coordinates that corresponds to the ordered pair. It’s always a good idea to start at the origin. The x-coordinate tells you how many steps you have to take to the right or left on the x-axis. And the y-coordinate tells you have many steps to move up or down on the y-axis.
The ordered pair is found in the coordinate system when you move 3 steps to the right on the x-axis and 4 steps upwards on the y-axis.
The ordered pair is found in the coordinate system when you move 7 steps to the left on the x-axis and 1 step upwards on the y-axis.
To find out the coordinates of a point in the coordinate system you do the opposite. Begin at the point and follow a vertical line either up or down to the x-axis. There is your x-coordinate. And then do the same but following a horizontal line to find the y-coordinate.
Making Something Out Of Nothing
Many historians and scholars agree that zero as we know it first emerged from India. Although the concept of marking nothingness existed in several other cultures, like the Mayans and Babylonians, the ancient Indians were the first to treat nothingness as a proper numeral rather than simply a placeholder. Math writer Alex Bellos has suggested that India provided an ideal setting to make this leap: The concept of nirvana, or nothingness, was well-established, and the word used in ancient Indian philosophical texts to refer to nothingness was shunya, a word that would later mean zero.
As Bellos told the BBC, Every time when youre writing down a telephone number or a price of something that has a zero, youre actually writing down something that has almost 2,000 years of mystical symbolism.
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What Does The Word Rational Mean
According to Collins English Dictionary and the American Heritage Unabridged Dictionary of the English Language, the word rational is an adjective that can refer to someone who bases their decisions on reason rather than emotion. Rational beings and rational creatures have a sound mind and rational thoughts. This person is in full possession of their good judgment. Other things besides people can be rational, like rational creatures, a rational plan, a rational negotiator, a rational faculty, a rational plan, rational analysis, and more. These things all have common sense, or can solve intellectual problems through the process of rational inference. They make use of the mind and intellect to apply principles of logic and sound judgment to situations. Rational is three syllables ra-tion-al, and the pronunciation of rational is rænl.
Rational is also a term in mathematics which refers to a real number of quantities expressible as the ratio of two integers where the second integer is not equal to zero. All integers, polynomials, and fractions are rational numbers.
Different languages around the world use words that mean rational. In looking at this list of translations of rational from Word Sense, you may notice that a lot of these look and sound similar to the word rational. These are called cognates, which are often formed when two words have the same root or language of origin.
Examples Of Numerator In A Sentence
numeratornumerator San Diego Union-Tribunenumerator Forbesnumerator WSJnumerator WSJnumerator The AtlanticnumeratorNational Reviewnumerator Quanta Magazinenumerator Wired
These example sentences are selected automatically from various online news sources to reflect current usage of the word ‘numerator.’ Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.
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Sigma As A Summation Operator
This is commonly known as the sigma notation. In practice, the sigma operator is used in finance and accounting, managing balance sheets and in similar other instances where there is a need to add a series of numbers.
You will also see the sigma sign as a parameter in various well-known mathematical formulas. For example, it is used in the formula for calculating the Rayleigh distribution and Maxwell distribution. When used in conjunction with certain symbols, sigma can denote other functions such as the divisor function that consists of small sigma with a k in the subscript.
In physics, you will often come across terms like 2-sigma, 5-sigma, and so on. This is a further extension of the use of sigma for representing standard deviation. Sigma with a bigger number as a prefix signifies a relatively lesser deviation from a set value and vice versa. It is a technique used by scientists to measure the fluctuations in a set of data, and identify whether it was caused by a certain factor or was just a random error.
In biology, the lowercase sigma symbol was initially used to demonstrate the total life span of a multicellular unit in the bone marrow. However, its use in this respect is now obsolete.
How To Find Range
To find the range in a set of numbers, you must gather your data, organize the data from least to greatest, then subtract the smallest value from the largest value. You can find a range of positive numbers and negative numbers.
Steps for how to calculate range:
For example, if you read a biography, and wrote down how many pages you read each day, you could take the range:
To find the range, put the number of pages in order from least to greatest:
Subtract the smallest value from the greatest value:
The range of this data set is 9 s .
Let’s figure the range of the following set of real numbers. Below are five of the lowest-scoring games in NBA history, listed with teams and total game points:
- Washington Capitols vs. Pittsburgh Ironmen 89 points
- Fort Wayne Pistons vs. Minneapolis Lakers 37 points
- Washington Capitols vs. Detroit Falcons 83 points
- Boston Celtics vs. Pittsburgh Ironmen 90 points
- Boston Celtics vs. Washington Capitols 85 points
Go through the three steps to find the range of these five games:
89 points, 37 points, 83 points, 90 points, 85 points
1) Gather the data:
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Sigma Symbol Its Meaning And Uses In Math And Science
As the next part of our article series about the Greek symbols, we are having a detailed look at the sigma symbol today. What does the sigma symbol mean? How is it used in math and science? The answers to all these questions and more are in this detailed post about the sigma symbol, its meaning and uses.
How Can The Word Rational Be Used In A Sentence
The word rational can be used in many different sentences in the English language. Using words in a sentence is a great way to memorize their definitions. You can also try making flashcards or quizzes to test your knowledge of the definitions of many different words. Try using this word of the day in a sentence today. You never know, it might become one of your new favorites. Below are a couple of examples of the word rational to get you started.
Mora is an extremely rational person. She works in economic development with various formulae every day and utility to predict economics.
The student studied evolutionary biology because she thought it was a rational choice to direct her toward medical school, but she is much more interested in psychology, sociology, and political science. She wished she had not gone along with conformity and thought outside the box.
When they were studying rational numbers and the quotient of integers in math class, the student became very confused. Why would they study imaginary numbers if they did not exist? He only understood math when it was wholly concrete.
Overall, the word rational means thinking with a sound mind or logic rather than emotions or feelings. This is also a term in mathematics that refers to integers and fractions that are not divided by zero.
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Chambers 20th Century Dictionaryrate This Definition:
ori-jin, n. the rising or first existence of anything: that from which anything first proceeds: the fixed starting-point: cause: derivation.adjs.Originable Original, pertaining to the origin or beginning: first in order or existence: in the author’s own words or from the artist’s own pencil: not copied: not translated: having the power to originate, as thought.n. origin: first copy: the precise language used by a writer: an untranslated tongue: a person of marked individuality.ns.Originality, Originalness, quality or state of being original or of originating ideas.adv.Originally.v.t.Originte, to give origin to: to bring into existence.v.i. to have origin: to begin.n.Origintion, act of originating or of coming into existence: mode of production.adj.Origintive, having power to originate or bring into existence.n.Origintor.
What Is The Definition Of Mathematics
Mathematics simply means to learn or to study or gain knowledge. The theories and concepts given in mathematics help us understand and solve various types of problems in academic as well as in real life situations.
Mathematics is a subject of logic. Learning mathematics will help students to grow their problem-solving and logical reasoning skills. Solving mathematical problems is one of the best brain exercises.
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