TUGAS SEJARAH MENGENAI KONSEP MATEMATIKA ATAU PENYELESAIAN MATEMATIKA PADA ZAMAN KUNO YANG MASIH DIPAKAI/TIDAK PADA ZAMAN SEKARANG ATAU SEBALIKNYA.

1. Yang saya temukan konsep matematika, persoalan matematika pada zaman kuno yang sekarang masih dipakai yaitu konsep matematika dan penyelesaian matematika antara lain:

v  KONSEP BILANGAN NOL : konsep bilangan nol ditemukan pada zaman kuno di India. Waktu itu bilangan nol hanya sebagai lambang. Dalam zaman modern, angka nol digunakan tidak saja sebagai lambang, tetapi juga sebagai bilangan yang turut serta dalam operasi matematika.

         Kini, penggunaan bilangan nol telah menyusup jauh ke dalam sendi kehidupan manusia. Sistem berhitung tidak mungkin lagi mengabaikan kehadiran bilangan nol, sekalipun bilangan nol itu membuat kekacauan logika. 

v ARITMATIKA : Sejak masa sebelum masehi, misalnya jaman Mesir kuno, cabang tertua dan termudah dari matematika (aritmetika) sudah digunakan untuk membuat piramida, digunakan untuk menentukan waktu turun hujan, dsb. Dan sampai sekarang ilmu mengenai aritmatika pun masih tetap dipelajari dalam pembelajaran matematika ataupun ilmu yang lain. Kemampuan aritmetika sudah cukup untuk mencari solusi (jumlah penduduk) dengan keakuratan yang cukup tinggi.

v MATEMATIKA MURNI : Banyak cabang matematika yang dulu biasa disebut matematika murni, dikembangkan oleh beberapa matematikawan yang mencintai dan belajar matematika hanya sebagai hoby tanpa memperdulikan fungsi dan manfaatnya untuk ilmu-ilmu lain. Dengan perkembangan teknologi, banyak cabang-cabang matematika murni yang ternyata kemudian hari bisa diterapkan dalam berbagai ilmu pengetahuan dan teknologi mutakhir.

2. Yang saya temukan mengenai konsep matematika, persoalan matematika atau penyelesaian matematika pada zaman kuno ada yang tidak dipakai pada saat ini adalah :

Menurut saya, bahwa pada zaman kuno menghitung luas lingkaran menggunakan π (phi) yang besarnya 3,16, namun sekarang besar phi zaman dulu sudah digunakan lagi. Dalam mencari luas lingkaran sekarang menggunakan π (phi) yang besarnya adalah 3,14.

3. Yang saya temukan konsep matematika, persoalan matematika atau penyelesaian matematika pada saat ini yang tidak ada hubungannya dengan matematika zaman kuno sama sekali adalah :

Menurut saya, bahwa sekarang banyak ditemukan konsep mengenai matematika yang tidak ada hubungannya dengan jaman dahulu misalnya mengenai closed problem, open-ended problems, open problems.

TAMBAHAN :

Peralatan Matematika yang digunakan pada jaman dahulu dan sekarang :

Dulu:

Abacus

Tulang Napier, Jangka sorong

Penggaris dan Kompas

Perhitungan biasa

Sekarang:

Kalkulator dan komputer

Bahasa pemrograman

Sistem komputer aljabar (listing) Notasi sederhana Internet

Analisis statistik software

- SPSS

- SAS

- R

KONSEP BILANGAN NOL
(pada jaman dulu dan sekarang)

Semua bilangan, nol atau bukan nol, rasional atau tak rasional, sudah ada DI DALAM PIKIRAN setiap manusia yang bisa berhitung. Yang belum ada adalah denotasi atau pelambangan bilangan tersebut, baik secara tertulis atau secara lisan, maupun dalam bentuk lambang-lambang yang kita kenal sekarang.
Bukti sejarah hanya memperlihatkan bahwa bilangan 0 ditemukan pertama kali dalam zaman Mesir kuno.
Waktu itu bilangan nol hanya sebagai lambang. Dalam zaman modern, angka nol digunakan tidak saja sebagai lambang, tetapi juga sebagai bilangan yang turut serta dalam operasi matematika.

Kini, penggunaan bilangan nol telah menyusup jauh ke dalam sendi kehidupan manusia. Sistem berhitung tidak mungkin lagi mengabaikan kehadiran bilangan nol, sekalipun bilangan nol itu membuat kekacauan logika.
Pelajaran tentang bilangan nol, dari sejak zaman dahulu sampai sekarang selalu menimbulkan kebingungan bagi para pelajar dan mahasiswa, bahkan masyarakat pengguna. Mengapa? Bukankah bilangan nol itu mewakili sesuatu yang tidak ada dan yang tidak ada itu ada, yakni nol.
Bilangan nol itu tidak selalu ditafsirkan sebagai sesuatu yang tidak ada. Sesungguhnya, setiap konsep dan entitas matematika, hanya berperan SEBAGAI MODEL dari suatu fenomena atau fakta nyata.

NUMBER CONCEPT of ZERO
( at era first and now)

All number, zero or non zero, rational or do not be rational, have IN MIND each;every human being which can calculate. What not yet there is denotation or the number device, either through written or verbally, and also in the form of device which we recognize now.
History evidence only show that number 0 found first time in ancient Egypt epoch.
At that time number of zero only as device. In modern epoch, number of zero used not even as device, but also as number which have a share in mathematics operation
Nowadays, number use of zero have infiltrated far into human life joint. System calculate no longer possible disregard the number attendance zero, even if number of zero that kick up a rumpus the logic
Lesson about number of zero, from since former epoch hitherto always generate the muzziness to all student and student, even consumer society. Why? Isn'T it true that number of zero that deputize the something that no and which is there no that there is, namely zero.
Number of zero that do not always interpreted by something that of there no. Real, each;every concept and entitas mathematics, only MODEL personating from a[n real fact or phenomenon.

FOUNDATIONS OF MATHEMATIC

Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. Mathematics at least develop; builded pursuant to one premis (or some premis) and one order (or some order) prosedural, or at least early from a certain dot. Premis starting point which must accepted what the existence of. Mathematics science in principle can be re-traced at basal logic principles.

IDEALISM PLATO

Figure of idealism is Plato ( 427-374 SM), student from Sokrates. Idealism teaching represent phylosophy teaching idolizing soul. According to him, goal is genuiness picture which solely have the character of the spirit and soul in among original picture with the shadow of a world of be under arrest by the five senses. Meeting of among soul and goal bear day-dream that is world idea. This teaching look into and also assume that real only idea. Idea by xself always remain to or do not experience of the change and also displacement, natural of motion not categorized by idea.
Existence Idea do not see in the form of physical, but original picture can only be made a picture by pure soul. In the eyes of idealism is picture from world idea, its position cause do not remain to. While such by idea pure reality and genuiness. Its existence very absolute and its perfection very absolute, cannot be reached by material. Practically, idea depicted with a world of do not the in form of that way soul have place in a world of body do not told by world idea
Concerning highest truth, with the famous doctrine with the idea term, Plato open that this world remain to and its type one, while highest idea is kindliness. Idea duty is lead the kindness of human being in becoming example for experience. Whosoever mastered the idea, he will know the definitive truth, so that can us as the appliance to measure, to grouping and assessing everyday natural everything.
Its principle, idealism teaching constitute all that ther. The real in this world only idea, idea represent the spiritial place and its for unlike real nature such as those which see and drawn. While its column don't have the most recently fulcrums and boundary from idea is arche representing place return the perfection of so-called world idea with the God, arche, everlasting in character and a few/little even also do not experience

GROWTH MATHEMATICS IN SOME PLACE

1. MESOPOTAMIA
a. Using algebra for the system of modern denary.
b. Finding heavy and measure system
c. The first which find “number system”
d. Influencing mathematics yunani.

2. BABILONIA
a. Using denary system and π = 3,125
b. Inventor calculator for the first time.
c. Aritmatika grow and expand very well become the algebra retoris.
d. Using geometry for astronomical calculation bases.

3. ANCIENT MESIR
a. Using Phytagoras theorem
b. Using number of papyrus moskow.
c. Using much formulas for calculate wide
d. Using number system base on 10 in the year 3000 SM.

4. ANCIENT YUNANI
a. Pythagoras non one who find the theorem pythagoras but he only succeed to make the best verification.
b. Hipassus of Inventor of number irrasional
c. Archimedes study about flat geometry
d. Recognizing prime number

5. INDIA
a. Brahmatya was born in 589-660 Ad.
b. Aryabatha ( 498 SM) finding relation circle a circle
c. Introducing usage of zero and number denary
d. Bhamatyagupta find the negative number

6. CHINA
a. Recognizing right triangle characteristic
b. Ancient mathematics China strength lay in the algebra
c. Have used the negative number far before culture of other;dissimilar
d. Organic culture cause weak at stiff verification

FIGURES OF MATHEMATICIAN

1. Thales
( 624-550 SM )
Thales is a mathematics formulating theorema or proportion, and explainable more detail by Euclid. Basis for mathematics as applied sciences seemingly have been opened by Thales, before emerging Pythagoras making number

2. Pythagoras
(582-496 SM)
Pythagoras is one who first triggering axiom require to be formulated beforehand in developing geometry.
Pythagoras non one who find the theorem pythagoras but he only succeed to make the best verification.

3. Diophantus
(200 – 250 SM)
Diophantus often conceived of by Mr. algebra Babylonia. Its masterpiece differ from the geometry algebra started by Euclid. Diophantus develop the concepts of algebra Babylonia and start an equation form so that form this equation oftentimes referred as with the equation Diophantine show that Diophantus enough give the influence for mathematics

4. Pappus
(290 – 350 SM)
Making ambit of all masterpiece, its predecessor especially masterpiece Apollonius with the quality more because its discussion have more detailed. A lot of idea Pappus weared by next era mathematics. Not many new idea which can be taken, but represent.

5. Plato
(427-347 SM)
Plato represent a big philosophy coming from yunani.
And Plato of teaching creator and also expert think first accepting understanding is existence of nature of non object.

6. Euclides
(325-265 SM)
Euclid represent the “geometry father” because finding number theory as well as geometry theory.
Subjects studied by euclid cover the forms, theorem pythagoras, algebraical equation, radian, space geometry, proportion theory, and others

7. Archimedes
(287-212 SM)
Principal Application archimedes of physics and matematics.
Calculation π (phi) in calculate area of circle

8. Appolonius
(262-190 SM)
Appolonius use the parabola concept, hyperbola, and ellipse which is a lot of giving contribution for modern astronomy

9. Abu Ja’far Muhammad ibn Musa Al-Khwarizmi
(780 – 850)
Act the Arabic mathematician really excrutiatingly. Inventor of algebra Term, giving base and bollard in mathematics. All that make he competent referred with the “ algebra father”, not Diophantus. Algebra teaching of with the elementary forms, Diophantus only have concentrated with the number theory. Algebra later; then learned and become the world property to date. Joining artimatika and algebra. Both important as especial source of mathematics knowledge during for centuries either in orient and also in West

STUDY HISTORY

Before we actually dive into this vast subject, I would like to touch on a few things. Firstly, studying history is like studying any other type of subject in that it demands participation and a big amount of patience. The successful student forces him or herself to study, of course there are certain tactics to make the whole thing go by easier and more effective.

Studying history is often perceived as boring… I have to disagree, it’s not just boring it is really boring if you don’t know how to tackle it! Here’s my take on the two elements you should always look at when studying history:

a) The Reasons/Causes behind an event
b) The Consequences that followed.

By understanding why things happened and what the events led to, you have in fact answered most of the questions. This is what any person studying history should look at, in contrast to getting caught on all the details. So the first action you need to take when you've received a new history assignment is to write down all the possible causes to the event and the consequences that erupted due to the causes.

You will find that most of the time, finding the consequences is by far easier than trying to understand why it happened in the first place.

PYTHAGORAS

Pythagoras adalah seorang ilmuwan yang jenius dan cerdas. Dia adalah anak dari Mnesarchus, seorang pedagang yang berasal dari Tyre.
Pythagoras dikenal sebagai pemikir baru pada jamannya dan dia dikenal sebagai guru besar yang penuh dengan charisma. Hal ini membuat banyak orang ingin berguru padanya. Dia juga memiliki falsafah paling penting yaitu “angka”.
Angka nol dalam kinerja Pythagorean tidak dikenal dan tidak ada dalam kamus Yunani. Penggunaan angka nol dalam suatu nisbah adalah hal yang melanggar hukum alam.
Rumus Pythagoras ( a2 + b2 = c2) yang kita kenal, itu sebenarnya bukan Pythagoras yang menemukan. Namun Pythagoras adalah orang yang berhasil membuat pembuktian yang paling baik dan dapat diterima.
Bilangan irrasional juga merupakan masalah bagi Pythagorean. Bilangan irrasional muncul karena ada rumus : a2 + b2 = c2. Bilangan irrasional ini adalah sebuah rahasia dan harus tetap dijaga, karena apabila hal ini terkuak akan menimbulkan masalah yang besar. Namun munculnya bilangan irrasional ini tidak dapat dihindari keberadaannya. Bilangan ini akan selalu ada pada semua bentuk geometri.
Ternyata rahasia ini terkuak juga, karena salah satu pengikut Pythagoras yaitu Hippasus. Kemudian Hippasus dijatuhi hukuman mati.


PYTHAGORAS

Pythagoras is a man of science who genius and smart. He is child from Mnesarchus, a merchant coming from Tyre.
Pythagoras known as a new thinker in his year and he wellknown a professor which is full of charisma. This matter make the many people wish to learn at him. He also own the philosophy most important that is " number".
Number of zero in performance Pythagorean is unknown and no in Greek dictionary. Number Use zero in ratio is matter which impinge the natural law.
Formula Pythagoras ( a2 + b2 = c2) what we recognize, that in fact non Pythagoras finding. But Pythagoras is one who succeed to make the acceptable and best verification
Irrational number also represent the problem for Pythagorean. Irrational number emerge caused by formula : a2 + b2 = c2. Irrational number is a secret and have to remain to be taken care of, because if this matter opened will generate the big problem. But this Irrational number appearance cannot be avoided by its existence. This number there will always at all of geometry form.
In the reality this secret opened too, because one of follower Pythagoras that is Hippasus. Later;Then Hippasus fallen by capital punishment

1658-CHRISTOPER WREN MENUNJUKKAN BAHWA PANJANG SUATU SIKLOID ADALAH EMPAT KALI GARIS TENGAHNYA SEBUAH LINGKARAN

Sir Christoper Wren lahir pada tanggal 20 Oktober 1632 di East Knoyle, Widtshine, Inggris. Dia adalah seorang perancang Inggris, ahli astronomi, ahli geometrid an juga merupakan arsitek terkenal.
Wren masuk perguruan tinggi Wadham yang ada di Oxford dan dia belajar berdasar pada disiplin Aristotle dan disiplin berbahasa latin. Kemudian Wren berhasil lulus B.A apada tahun 1651 dan 3 yahun kemudian lulus M.A pada tahun 1653. Wren melakukan penelitian ilmiah dan salah satunya adalah metode transfuse darah yang ia lakukan pada 2 anjing. Selain itu dia juga meneliti tentang alat untuk mengukur sudut, mesin untuk menaikkan air, cara untuk menghitung jarak laut berdasarkan garis bujur, dan lain sebagainya.
Dan pada tahun 1657, dia ditetapkan sebagai Profesor astronomi Gresham College, London. Dan dia juga melakukan penelitian mengenai planet Saturnus sekitar tahun 1652. Dan dia dapat menjelaskan penemuannya mengenai pemusatan matahari dan planet-planet dengan menggunakan teleskop.
Wren merupakan salah satu matematikawan, dia berhasil menemukan bentuk geometri, salah satunya adalah tentang sikloid. Pada tahun 1658, Christoper Wren menyatakan bahwa panjang sikloid yaitu empat kali diameter lingkaran pada umumnya. “Sikloid” adalah kurva yang didefenisikan sebagai bagian dari ujung tepi roda lingkaran yang berputar sepanjang garis lurus.
Tidak diragukan lagi, Wren mempunyai peran penting dalam Royal Society karena keahliannya dalam berbagai bidang dan membantu para ilmuwan lainnya bertukar ide dalam melakukan berbagai penelitian.

1658-CHRISTOPER WREN SHOWS THAT THE LENGTH OF A CYCLOID IS FOUR TIMES THE DIAMETER OF ITS GENERATING CIRCLE

Sir Christoper Wren was born at 20 October 1632 in East Knoyle, Widtshine, English. He is a designer from English, astronomer, expert of geometrid an also represent the famous architect.
Wren studied at Wadham college of exist in Oxford and he learn to base on the discipline of Aristotle and discipline have Latin Ianguage too. Later; Then Wren succeed to pass the B.A in 1651 and 3 year later, he pass the M.A in 1653. Wren doing the research and one of them is method of transfuse blood which he doing at two dogs. Others he also check about appliance to measure the angle;corner, machine to boost up the water, way of to calculate the distance go out to sea pursuant to meridian, and others.
And in 1657, he is specified by as astronomical Professor of Gresham College, London. And he doing the research of concerning planet Saturnus in 1652. And he can explain its invention hit the concentration of sun and planet by using telescope.
Wren represent one of mathematics, he succeed to find the geometry form, one of them is about sikloid. In the year 1658, Christoper Wren express that length sikloid that is four times radian diameter generally. "Sikloid" is curve which definition as part of back part step aside the rotatory radian wheel as long as straight line.
No doubt again, Wren have the important role in Prodigal of Society because its membership in so many area and assist all other man of science change over the idea in doing various research.

1919-VIGGO BRUN MENDEFENISIKAN TETAPAN BRUN (B2) UNTUK PRIMA KEMBAR

Prima kembar merupakan bilangan prima yang berbeda dengan bilangan-bilangan prima yang lain. Contoh dari pasangan bilang kembar adalah 5 dan 7, 11 dan 13; dan 821 dan 823.
Kecuali untuk pasangan 2 dan 3, pasangan ini merupakan bilangan kecil diantara pasangan bilangan prima lain.
Viggo Brun adalah seorang matematikawan yang berasal dari Norwegia. Pada tahun 1919 Viggo Brun menunjukkan bahwa ada hubungan pada bilangan prima kembar untuk bilangan prima kembar dan biasanya dinotasikan B2.
Viggo Brun menggunakan metode penyaringan untuk menunjukkan bahwa bilangan prima kurang dari x adalah <
Dan teori penyaringan adalah serangkaian teknik umum dalam teori bilangnan yang dirancang untuk memperhitungkan atau lebih relitas untuk memperkirakan ukuran.

1919-VIGGO BRUN DEFINES BRUN’S CONSTANT B2 FOR TWIN PRIME

Twin Prime represent the different prime number with the other prime number. Follow the example of from couple spell out members the twin are 5 and 7, 11 and 13; and 821 and 823. Except for the couple of 2 and 3, this couple represent the small number among other;dissimilar prime number couple.
Viggo Brun is a mathematics coming Norwegian. In 1919 Viggo Brun indicate that there is relation of at prime number twin for the prime number of twin and usually notation B2.
Viggo Brun use the screening method to indicate that the prime number less than x [is] <<>
And screening Theory is with refer toing common technique in number theory designed to reckon or more relitas to estimate size measure.