PAPER OF HISTORY OF MATHEMATICS

HISTORY OF EXPONENT

By :
ST.MAISARAH
1911442011

DEPARTEMENT OF MATEMATICS
FACULTY OF MATEMATICSN AND SCIENCE
STATE UNIVERSITY OF MAKASSAR
2020
HISTORY OF EXPONENT NUMBERS

Basically exponents are not a number system or number type but rather a concept or
method of writing a number. We do not call exponents a number system such as whole
numbers, whole numbers, rational numbers, real numbers and so on, because they are
basically different. In everyday life we often encounter the multiplication of a number by the
same factors.
2 x 2 x 2 ...
4 x 4 x 4 ...
15 x 15 x 15 ...
22x 22 x 22 ...
The multiplication of numbers by the same factors as above is called repeated
multiplication. Each repeated multiplication can be written briefly by using the exponent
notation.

Definition of Exponent

Exponents are repeated products. The number of multiplications performed is written

over the base number with a small number size. For example: 2 x 2 x 2. Then write 23. With
2 as the base number, and 3 as the exponent (number of multiplication).

Figures and History of Exponential Numbers

1. John Napier 

In 1616 John Napier discovered: The decimal number. Example: 6.5 Reads six point
five and logarithms Example: 23 = 8 Equals 2log 8 = 3. Exponential numbers really help us
in shortening numbers that are relatively large or small. For example, 0.00000099 is written
as the powers of 9.9 10-7
 The person who first discovered exponents or exponents was John Napier (1550-
1617). John Napier was a nobleman from Merchiston, Scotland. John Napier is also the
inventor of logarithmic numbers, which do have something to do with exponents. John
Napier realized that every number can be changed in the form of exponents or logarithms, so
that the number can be converted into a simpler form.
John Napier was also a mathematician, physicist, astronomer, and astrologer. Notable
legacies in the field of mathematics include Napier's bones or rabdologia. Rabdologia comes
from the Greek rhabdos meaning stem and logia means learning. Rabdologia is a calculating
tool like an abacus that is used to perform multiplication and division calculations using the
basic concept of adding for multiplication and subtraction for division. Napier's bones consist
of a board with a border and a set of bars with written numbers on it. Boards and bars are
usually made of wood, metal or thick cardboard.

A set of Napier's bones (Rabdologia) and an example of a 7 times list.

However, without using such rabdology we can still use the concept of Napier's bones count
to perform a multiplication or division count. The following is an example of calculating
multiplication using the concept of calculating in rabdology.

Example: 15 X 13 =. . .
To complete the two-digit multiplication, first draw four squares to represent the digits being
multiplied as follows:

Step 1

Draw four squares with each square divided in half with a diagonal line. Since we are
multiplying 15 by 13, then:

Step 2

Multiply each digit of the number, and write the result in the appropriate box. Notice
how to put the product of the numbers. One square is divided by two parts by a diagonal line,
the top of the diagonal is filled with tens digits, and the bottom of the diagonal is filled with
ones digits. So, if the product is a one-digit number, 0 is written at the top of the diagonal,
and that one digit (unit) is stored at the bottom of the diagonal.

1 x 1 = 1 (written 01 in row 1, column 1)

5 x 1 = 5 (write 05 in the row 1 box, column 2)
5 x 1 = 5 (write 05 in the row 1 box, column 2)
1 x 3 = 3 (written 03 in row 2, column 3)
5 x 3 = 15 (write 15 in row 2, column 2)

Step 3
After all the boxes are filled, it's time to add up each number according to the position
of the diagonal line. We will add up starting from the bottom right hand corner.
5 (for unit digits)
3 + 1 + 5 = 9 (for tens digit)
0 + 1 + 0 = 1 (for hundreds of digits)

The product is written on the bottom and left side of the box. In order, from the
bottom right corner to the left are the ones digit and tens digit, and on the lower left side are
the hundreds digit. There is no thousand digit There is no thousands digit, because the
number in the upper left corner is 0.
So, 15 x 13 = 195

 2. Rene Deskrates
 The method of writing repeated multiplication using exponential notation or
exponential notation was first introduced by one of the French mathematicians Rene
Deskrates (1596–1650). In the 16th century, Italian mathematicians used the term lato
(meaning "side") which was sometimes interpreted as a root because the side was unknown in
length. This term then taken to calculate the side length of a square and the squared number
is called lato cubico.

Bombelli uses terminology using the symbol R., meaning radix, but is similar to the
universal symbol commonly used by doctors in prescribing. Therefore, Bombelli later
replaced it with the symbol R.q. (radice quarata), so that the square root for 2 is written with
the notation R.q.2 and the cubic root for 2 is written with the notation R.c. 2 (radice cubica).
The symbols above began to be used by Bombelli in his famous book L'Agebra.

Writes root notation with R.q. or R.c. turned out to be inconvenient and impractical so
it was written in the form of r (lowercase r). What happened then? Writing the notation with r
is if it is written by hand (not a typewriter), especially if the person's writing is bad, then what
appears is an unusual shape. Over time the various small r letters were given the standard
form, namely the form as we know it today, namely √. Before people used x² as the symbol
for xx, x³ as the symbol for xxx and so on, people used to find it difficult to write an equation
with more than one degree. At that time, the symbols x, y, z and so on were already used to
represent numbers with no known value. However, when they are faced with high power
numbers such as n, it is very impractical to write it in the form of multiplying x n times. Thus,
simple symbols are needed for these numbers. In the 17th century French mathematician
Rene Descartes was the first to use a, b and c to express numbers whose values have known.
At that time, Descartes began to use the symbol x² for xx and so on. Since then algebraic
equations have been written in modern form.

3.  Mishael Stifel

The exponent comes from two syllables from the other languages "Expo" and
"Ponere". Expo means originating or from and Ponere where he himself. The use of the word
exponent in modern mathematics was first recorded in the book "Arithemetica Integral"
written by an English mathematician named Michael Stifel. However, at that time the term
exponent was only used for the base number 2.So the term exponent 3 means 23 which is
worth 8.
 The initial appearance of the exponent is not exactly clear. Although not 100%
correct, many say this system of rank or exponential has existed since Babylonian times. In
the 23rd century BC the Babylonians around the Mesopotamian region had known squares in
their calendar system.

The concept of the exponent in modern times differs somewhat from that of the Stifel or of
Babylonian society. The exponent is now used to determine the number of times the number
is multiplied by itself. With the exponent you no longer need to write 3 x 3 x 3 x 3 x 3 x 3 x 3
x 3 x 3 x 3 x, you just have to write 310.

How to apply the exponential material in the scope of the school

Exponential is a repeated multiplication operation with the same number, for example 43 = 4
x 4 x 4 shows the repeated multiplication of three numbers 4. Numbers that are repeatedly multiplied
are called base numbers, while numbers that show the number of principal numbers that are
repeatedly multiplied are called exponents or exponents. So 4 is the base number and 3 is the
exponent.

While the exponential function is a function that contains the exponential form with the
power in the form of a variable. The function of exponents is widely used in everyday life such as
plant growth, radioactive decay, and so on.

The exponential function with the principal numbers a, a> 0 and a ≠ 1 has the following general form:
f: x ax or y = f (x) = ax

Description: a is the base number (base), x is the exponent or exponent number

The graph of exponential functions can be graphed on Cartesian coordinates in the same way
as drawing other functions. For example, graph the exponential function f (x) = 3x! To graph the
function graph, first determine the coordinates of several points that the function graph passes. Below
are the coordinates of the point through which the graph of the function f (x) = 3x passes.

F (x) = 3x

x Y = f (x)

-1

0 1

1 3

2 9

Exponential Equations
 An exponential equation is an equation that contains an exponential form. In this
equation the exponential value that satisfies the equation can be determined. Where, the
exponential value that satisfies this becomes a member of the set of solutions to the
exponential equation. Consider the following example:

42x-1 = 32x-3 is an exponential equation whose exponent contains the variable x

(y + 5) 5y + 1 = (y + 5) 5-y is an exponential equation whose exponent and base number

contains the variable y 16t + 2.4t + 1 = 0 is an exponential equation whose exponent contains
the variable t

There are 4 general forms of exponential inequality, including:

af(x) < ag(x)

af(x) ≤ ag(x)

af(x) > ag(x)

af(x) ≥ ag(x)

In addition, in solving the exponential inequality, 2 properties can be used, namely:

If a> 1, then af (x) ≥ ag (x) <—-> f (x) ≥ g (x) (sign of inequality does not change)

If 0 <a <1, then af (x) ≥ ag (x) <—-> f (x) ≤ g (x) (sign of opposite side inequality)

Exponential Functions Application

The exponential function with the principal number (base) e is often used to solve
problems in everyday life. As in biology, the application of the exponential function in this
field is usually used to count a bacterium.

In addition, this function can be used in the economic field, usually used in banking,
one of which is the calculation of compound interest. In addition, for the social sector, the
application of the exponential function is usually used in calculating population growth over
a certain period of time.
 REFERENCES
http://linkmath.blogspot.com/2016/06/sejarah-bilangan-eksponen.html

https://www.kelaspintar.id/blog/edutech/cari-tahu-lebih-jauh-tentang-fungsi-eksponensial-
5434