# Math History

## Far more interesting than one might first expect, the history of mathematics is filled with bitter rivalries, political machinations, and incredible innovations by some of the most amazing minds in history. Post all questions concerning individual mathematicians, the development of mathematical theories, and the sociological impact that resulted into this category.

###### Asked in Inventions, Math History

### Who invented the abacus?

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.

###### Asked in Numerical Analysis and Simulation, Math History

### What is the origin of the expression plus one?

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...

###### Asked in Math History

### When and who invented the abacus?

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.

###### Asked in Math History, Technology

### What is the 8x8 rule of slides?

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

###### Asked in Religion & Spirituality, Philosophy and Philosophers, History of Science, Math History, Scientists, Mathematicians, René Descartes

### Why did René Descartes believe in god?

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)

###### Asked in Math and Arithmetic, Geometry, Math History

### What is mathematical Pi?

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 pi
Pi 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).

###### Asked in Math and Arithmetic, Math History

### How was pi invented?

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)

###### Asked in Algebra, Math History

### What does the term first difference mean in math?

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), ...

###### Asked in Math and Arithmetic, Geometry, Math History

### What are objects that are obtuse?

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