Inventions

Math History

The first reported and substantiated use of an abacus, or abacus-like instrument was in Sumeria between 2,700 and 2,300 BCE - or roughly 4,700 years ago.

This used a table of columns with each column equivalent to an order of magnitude above the previous column; just as we would have columns for x10, x100, x1000, x10000.

During the next 2000 years various forms of this came into common usage across areas of the world (Mesopotamia, Persia, Egypt, India, China, Greece, Rome). Some were similar in appearance, while others used the same principals, but looked slightly different. For example the Roman abacus used a clay tablet with columns and counting stones (a counting board), while the Chinese version looked almost identical, but had fixed string columns with counting stones attached to them - similar how most people picture an abacus.

The spread and variance in design of the abacus is probably due to the movement of early traders across the early trade routes (Silk Road etc.). The abacus is still made extensive use of today, as they are simple to use, fast and don't require batteries to operate them. The word abacus comes to us by way of Latin as a mutation of the Greek word abax. In turn, the Greeks may have adopted the Phoenician word abak, meaning "sand," although some authorities lean toward the Hebrew word abhaq, meaning "dust."

Irrespective of the source, the original concept referred to a flat stone covered with sand (or dust) into which numeric symbols were drawn. The first abacus was almost certainly based on such a stone, with pebbles being placed on lines drawn in the sand. Over time, the stone was replaced by a wooden frame supporting thin sticks, braided hair, or leather thongs, onto which clay beads or pebbles with holes were threaded. A variety of different types of abacus were developed, but the most popular became those based on the bi-quinary system, which utilizes a combination of two bases (base-2 and base-5) to represent decimal numbers.

Although the abacus does not qualify as a mechanical calculator, it certainly stands proud as one of first mechanical aids to calculation.

Both the abacus and the counting board are mechanical aids used for counting; they are not calculators in the sense we use the word today. The person operating the abacus performs calculations in their head and uses the abacus as a physical aid to keep track of the sums, the carrys, etc.

What did the first counting board look like?

The earliest counting boards are forever lost because of the perishable materials used in their construction. However, educated guesses can be made about their construction, based on early writings of Plutarch (a priest at the Oracle at Delphi) and others.

In outdoor markets of those times, the simplest counting board involved drawing lines in the sand with ones fingers or with a stylus, and placing pebbles between those lines as place-holders representing numbers (the spaces between 2 lines would represent the units 10s, 100s, etc.). The more affluent people, could afford small wooden tables having raised borders that were filled with sand (usually coloured blue or green). A benefit of these counting boards on tables, was that they could be moved without disturbing the calculation- the table could be picked up and carried indoors.

With the need for portable devices, wooden boards with grooves carved into the surface were then created and wooden markers (small discs) were used as place-holders. The wooden boards then gave way to even more more durable materials like marble and metal (bronze) used with stone or metal markers.

There is no way that anyone can tell who invented the abacus. But it must have been first used as an intermediate way of noting the computation or count before commiting the final result on papyrus for the Egyptians, or on paper or whatever the Greeks used to write their records on.

Remember that the four fundamental operations would have been impossible on both Egypt and Greece's system of writing numbers, but notice that the system of numeration of both are forerunners of the Hindu base 10 system of numeration.

This means that the systems of writing numbers - Hindu, Greek, Egyptian, are in a sense the same. All three write numbers in the 1 to 9, 10 to 90, 100 to 900 patterns.

The numeration system of Greece and Egypt were the cumbersome to use that Rome decided to simplify the writing of numbers, limiting to IVXLCDM and the dash the symbols - overly simplyfying it but emphasizing all the more their need for the Roman Abacus to make their computations.

It could have been the Roman Abacus that served as inspiration to the Chinese Abacus, which is strictly speaking an Hexadecimal Abacus. The Polos, the uncle and father of Marco Polo, who reached China in 1272, must have introduced this innovation to the court of Kublai Khan. One account of the Chinese Abacus mentioned that it first came to notice in the 14th century which is 28 years from 1272. If the Suan Pan became widely used in the mid or late 14th century, that was just enough time for an innovation to filter below from the top, if we are to remember that the Hindu numeration the Arabs brought to Europe via Spain and Italy took several hundred years, from the time Leonardo of Pisa first mentioned it in his book in 1202.

The Filipino Abacus referred to in an earlier note and twisted to sound as if a Filipino invented the abacus, referred to a nine-beaded color-coded by period decimal Filipino Abacus.

637638639

Numerical Analysis and Simulation

Math History

The expression "plus one" simply means to add 1 to whatever it is applied to.

If you are referring to the "+1" sometimes found in comments on forum posts and the like, it is a reference to buttons labelled with "+1" or similar text, used to vote for the post or indicate a positive opinion of the post.

Addendum:

It's also possible that this question refers to the phrase as used on invitations - where the invitation is for the recipient and their guest. It can be used when you wish to invite someone to a function and aren't sure of who they're currently seeing...

483484485

Math and Arithmetic

Mountains

Math History

The Difference Between

What you do is that you subtract the smallest number & the largest number. For example: The numbers 24, 47, 78, & 36. Okay so the largest is 78 and the smallest is 24. So 78-24=54. 54 will be your range.

116117118

Math History

The first reported and substantiated use of an abacus, or abacus-like instrument was in Sumeria between 2,700 and 2,300 BCE - or roughly 4,700 years ago.

This used a table of columns with each column equivalent to an order of magnitude above the previous column; just as we would have columns for x10, x100, x1000, x10000.

During the next 2000 years various forms of this came into common usage across areas of the world (Mesopotamia, Persia, Egypt, India, China, Greece, Rome). Some were similar in appearance, while others used the same principals, but looked slightly different. For example the Roman abacus used a clay tablet with columns and counting stones, while the Chinese version looked almost identical, but had fixed string columns with counting stones attached to them - similar how most people picture an abacus.

- The spread and variance in design of the abacus is probably due to the movement of early traders across the early trade routes (Silk Road etc.).
- The abacus is still made extensive use of today, as they are simple to use, fast and don't require batteries to operate them.
- The word abacus comes to us by way of Latin as a mutation of the Greek word abax.
- In turn, the Greeks may have adopted the Phoenician word abak, meaning "sand," although some authorities lean toward the Hebrew word abhaq, meaning "dust."

Irrespective of the source, the original concept referred to a flat stone covered with sand (or dust) into which numeric symbols were drawn. The first abacus was almost certainly based on such a stone, with pebbles being placed on lines drawn in the sand. Over time, the stone was replaced by a wooden frame supporting thin sticks, braided hair, or leather thongs, onto which clay beads or pebbles with holes were threaded. A variety of different types of abacus were developed, but the most popular became those based on the bi-quinary system, which utilizes a combination of two bases (base-2 and base-5) to represent decimal numbers.

Although the abacus does not qualify as a mechanical calculator, it certainly stands proud as one of first mechanical aids to calculation.

465466467

Math History

10 times 10 equals 100

different answer

25X4=100

20X5=100

50X2=100

100101102

Math and Arithmetic

Geometry

Math History

It is called a Hexagon. [Hecks-uh-gon]

A hexagon has 6 sides.

Hexagon

A hexagon.

Equal sides a hexagon

Hexagon

hexagon

hexagon

hexagon

A hexagon has a total of six sides. It also has a total of six internal angles.

A six sideded polygon is a hexagon.

A six sided polygon is an hexagon

160161162

Math History

Technology

The following is an example of 8x8

the rule is to have

no more than eight lines of text per slide

and no more than eight words per line.

8 x 8 rule is to help us to

not overwhelm our audience

ensure that they can read the text.

works if you use only key words / phrases.

or in paragraph format.

the 8 x 8 rule of slides is to help us not to overwhelm our audience with too much information and it should ensure that all the members of your audience can view and read the text. the rule is to have no more than eight lines of text per slide and no more than eight words per line. You should be able to stick to this simple rule if you use only key words or phrases.

what is easier to read and get the main point quickly

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Math History

Mathematicians

He is known for quartic equations.

336337338

Math and Arithmetic

Geometry

Math History

Pi is a mathematical ratio symbolized by the Greek letter π.

Pi (symbol π ) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. (Area of a circle = πr2)

This number is the same for every circle. This means that for any circle, the length of the circumference divided by the length of the diameter equals pi. It's expressed in the formula pi = C/d , usually written as C = pi x d , finding the circumference when the diameter is known. The concept has been handed down for thousands of years, and it developed alongside mathematics for much of that time.

The exact value of pi can never be expressed exactly in numerical form. This is because pi is a transcendental number; it is irrational. But here are its first few digits (for more digits, see the discussion page):

3.1415926535897932384626433832795028841971693993751

Because pi is a non-repeating, non-terminating number, it is often approximated as 22/7, or 3.14, or 3.1416 in order to make calculations a little more manageable. As a fraction, its closest approximations for basic mathematical purposes are 22/7, 333/106 or 355/113.

As a decimal figure, 3.14 or 3.14159 are most generally used.

Pi is the ratio of the circumference of a circle to its diameter.

π is an irrational number, which means that its value cannot be expressed exactly as a fraction, Consequently, its decimal representation never ends or repeats.

Other properties of piPi isn't just about circles. It's not even just about geometric shapes. For instance:

* pi/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - ...

* pi^2/6 = 1/1 + 1/4 + 1/9 + 1/16 + ... (the denominators are the square numbers)

* Pi appears in complex analysis, in a formula which expresses the nth derivative of a function as an integral.

* It also appears in Fourier analysis - the mathematical theory which allows us to, for instance, take a sound wave and calculate how much of it is at each frequency.

* In probability theory, the probability density function for the (normalized) normal distribution is exp(-x^2/2)/sqrt(2*pi).

293294295

Algebra

Math History

Maths studies is easier, hence some universities don't recognise it. But it really depends on what you want your future career path to be, if it's something completely not related to math like being an artist, then sure choosing math studies will be fine.

305306307

Religion & Spirituality

Philosophy and Philosophers

History of Science

Math History

Scientists

Mathematicians

René Descartes

One of his reasons for believing in god is that he knows (or thinks) that God is perfect. Since perfection includes existence, he therefore assumes that God must exist.

Answer:

Descartes made a series of increasingly unsupportable suppositions to back up his beleief in God:

1. I exist (A supportable statement for an individual - Cogito ergo sum)

2. I have in my mind the notion of a perfect being (The idea that anyone can develop an idea of a perfect being is not provable. The Aztec may have thoght their bloodthirsty gods perfect as well)

3. An imperfect being, like myself, cannot think up the notion of a perfect being (There is no proof although it is believable that humans are not perfect and it is debatable if the idea he has of a perfect being is indeed perfect)

4. Therefore the notion of a perfect being must have originated from the perfect being himself (This is a flight of fancy)

5. A perfect being would not be perfect if it did not exist (Buddhists, for example see perfection in the loss of being)

6. Therefore a perfect being must exist (This does not follow from any of the above statements)

312313314

Math and Arithmetic

Math History

It was discovered by the fact that the circumference of any circle when divided by its diameter is equal to pi.

The earliest evidenced conscious use of an accurate approximation for the length of a circumference with respect to its radius is of 3 + 1/7 in the designs of the Old Kingdom pyramids in Egypt. The Great Pyramid at Giza, constructed c.2550-2500 BC, was built with a perimeter of 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≈ 2π

(Courtesy of Wikipedia, Pi)

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Math and Arithmetic

Math History

The first Pi Day was organized by Larry Shaw in 1988. Check the related links for more information.

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Math History

Mathematicians

Dr. Srinivasa Ramanujan was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made substantial contributions to mathematical analysis, number theory, infinite series and continued fractions.

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Math and Arithmetic

Math History

Isaac Newton and Göttfried Leibniz simultaneously and indepently created calculus as we know it and derivatives with it. (Late 17th century)

263264265

IQ

Math History

Law School

move closer to the edge of the bed so you can drop off

122123124

Algebra

Math History

The phrase "first difference" is usually associated with a sequence of numbers: a(1), a(2), a(3), a(4), ... . The sequence may have a simple rule for generating the numbers , a complicated rule or, if it is a random sequence, no rule at all.The sequence of first differences is a(2)-a(1), a(3)-a(2), a(4)-a(3), ...

239240241

Jonas Brothers

Length and Distance

Math History

Pyramids

1000 millimetres or 3ft 3.37 inches

239240241

Math and Arithmetic

Geometry

Math History

objects that are obtuse are the minute hand on the 9 and the hour hand on the 6 on a clock, the field of a baseball tournament (diamond), corners a house, a garage is shaped like a trapezoid so there's an obtuse angle between the front and one side of a garage, and matel piece above the fire place. im a really smart person, i answer many questions, some people vote me for smartest family member. im not a nerd, im awesome so yeah. im pretty too, ill show a pic if i could on the next update on an unanswered question. i hope you understand this!

<3

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