THE PAST AND THE PRESENT

                                             

 Some weeks ago, our lectures Mr. Marsigit give a job. He orders us to search the mathematics concepts, mathematics problems and also mathematics solutions. 

1. The mathematics concepts, mathematics problems and mathematics solutions from the past and is still used by us are:

• Sexagesimal (base-sixty) is a numeral system with sixty is the base. In the first, this system used by Sumerians in the 2000s BC and Babylonians. It is still used for measuring time, angles and geographic coordinates.

The ancient uses:
 The ancient Mesopotamia uses the sexagesimal but it’s not a pure base 60 systems, in the sense that it didn’t use 60 distinct symbols for its digits.
 In the Chinese calendar, a sexagenary cycle is commonly used 

 Base-60 number systems have also been used in some other cultures, for instance the Ekagi of Western New Guinea. 

The modern uses:
 Unlike most other numeral systems, sexagesimal is not used so much in modern times. This numeral system is used in measuring angles, geographic coordinate and time. 
One hour of time is divided into 60 minutes and one minute is divided into 60 seconds. 

The practical unit of angular measure is degree, of which there are 360 in a circle. There are 60 minutes of arc in a degree and 60 seconds of arc in a minute. 

• Zero number concept. This concept, firstly used by Aryabhata from India. He use zero in calculation system and just not empty place. Now, we still use this concept in integers.

• Pythagoras prove a theorem that hypotenuse square of right angled triangle is the total square from two other sides. And now, we still use this theorem which usually named Pythagoras theorem.

• In the Pythagoras period appear a problem which can’t finished by rational number. If a flat line with point 0 and 1, point 0 lie in the left 1 and the negative lie in the right 1. Then q fraction can show with point which divided each unity in the same part of q. The problem is there is point at the line which can’t represent by rational number. So, they must create a new number to show this number, from this problem the irrational number was born. For a several time the root of two is the only one of irrational number. Then the opinions from Plato and Theodorus that the roots of 5,7,8,11,12,13,14,17 are the irrational number too.
  

2. The mathematics concept, mathematics problems and mathematics solutions from the past and not used by us are:

• Rhind papyrus explains that a square area is square from 8/9 of diameter. From this formula, we can get phi= 3,1604…., but now we use phi= 3,14.

• Aryabhata give a pyramid volume is a half of total base times high and sphere volume is phi3/2 .phi3 . Hindu’s people also give several value to phi but they usually use phi=3 and phi=10.
 
3. The mathematics concept, mathematics problems and mathematics in the present which not found in old period are:
• There are many problems in the present that can’t finished with old theorem like closed problem, open-ended problem and open problem. 



Reference: 
• http://wikipedia.com
• The history of mathematics

Speech by Mr. Marsigit

In here, I want to retell what Mr. Marsigit says. Some weeks ago, he tells us about history of mathematics.
History leaving two things:
•Artifacts : something that have form
•Ideas : something that come from mind
There are three streams to explain history:
•Real
•Ideal
•Contemporary
There are some problems to study history:
•The old document
Solution: with internet, we can get new document, which contains the old document.
•Translation
oContext ( geographical, time, society and culture)
oMethodologies
oBearing with other science
There are some manners to study mathematics:
•Empiric: observation, draw a conclusion with induction
Example: Pythagoras develops a theory, then we calls theorem of Pythagoras. The function is c2 = a2 + b2 , then emerge problem, which call irrational number.
•Deduction: this manner develop by Euclid’s, he created book calls “the elements” consist of 13 books containing what referred as definition, postulate or axiom or theorem. Euclid also called as father of mathematics axiom.
Infinite regress is meaning rotation which is no ending.
Aristotle: an elementary assumption preceding a definition. An elementary assumption is a foundation of mathematics.
There are two worlds in mathematics:
•Believe that mathematics have a reason
•Disbelieve that mathematics have a reason
Immanuel Kant said that mathematics must have dynamic foundation. He said that mathematics has foundation calls epistemology but in fact, epistemology is knowledge has not any foundation. Epistemology is a science studying sources of knowledge.
Hill Bert develops a formal mathematics with the logical foundation. Mathematics developed becomes a system having characters deductive and formal.
Hill Bert has a student named Kurt Gödel, he proving complete and incomplete axiom. If mathematics desired consistence, it can be incomplete and if mathematics desired complete, it can be inconsistence.
Plato is an idealist; he said that mathematics stay in kept quiet mind. A way so that we can think is exit from Plato Cave (darkness). Mathematics is given by God.
Aristotle said that mathematics based experience so it is stays out of mind. Mathematics is created by human.
Immanuel Kant: mathematics built with critical mathematics.
Mathematics having character synthetic a priori: we can think it although we never see it.
Synthetic  mathematics as mathematics, experience and ideas.
The opposite of a priori is a posteriori: we see it and then we think it. The law of synthetics is contradiction, in ideas can result a science.
The opposite of synthetics is analytics. The law of analytics is identity.
The constant mathematics foundation is geometry.
The old of mathematics foundation is set.
Mathematics based on intuition.
Common people  intuition is a feeling
Intuition is a place of the nesting fact of mathematics.
Brower is an intuition figure; he is not taking any reason. Intuition is a place or framework: space and time. It means that my mind about mathematics stay in space and time.
The absolute mathematics: mathematics is always true.
The language mathematics: the wrong mathematics is still mathematics.
Many versions about mathematics:
•System
•Structure
•Language
•Body of knowledge