Interview Of Euclid Ammar: Hi Mr. Euclid. Euclid: Hello Ammar: How are you Sir? Euclid: I am fine thank you. Euclid: How may I help you. Ammar: I want an interview of you Sir for my history teacher.

May I get it? Euclid: Yes, sure, why not. So what do you want to ask me? Ammar: If you wont mind, can I ask some personal questions in the beginning of the interview? Euclid: OK! I wont mind unless they are too personal. Ammar: What date were you born, and where were you born? Euclid: I am not sure about my date of birth because in those days there were no birth certificates and our parents dont keep record of the dates of births. I believe I was born around 300 BC. I was born in Alexandria, Athens, Greece. Ammar: Did you marry? How many kids do you have? Euclid: Well, I married and I have two kids. The eldest on is a boy and the younger one is a girl. Ammar: What school you went to? Tell us something about it.

Euclid: I went to Alexandria School. It is situated in Athens, Greece. The teachers of that school were the pupils of Plato. After I graduated from that school I started teaching in that school. After working for a while I created a school of mathematics and then I started teaching there.

Ammar: Were you interested in mathematics since the beginning of your studies or you changed your mind later? Euclid: At first when I joined school and I had no idea of what I will become. I dont know what happened and I later became interested in math and I thought of becoming a mathematician. Ammar: During the time you were in school, there were very famous Greek Philosophers like Socrates, Aristotle, and Plato. They also had many different followers, who do you think you follow? Why? Euclid: I think I belong to the persuasion of Plato because I was taught by his pupils and the ideas in me are quite platonist. You could see that by reviewing the results of my researches (Proculs, p. 57[68:19-20]; Bulmer-Thomas, p.415).

Ammar: What contributions you made in mathematics? Euclid: You know that I devoted my whole life in the field of math and I think all of my works are a contribution to the field of math. All of my works are combined in form of books. They are Elements, Data, On Divisions of Figures, Phaenomena and Optics. Ammar: Tell us something about your book Data. Euclid: The Data is closely related to the first four books of the Elements. It opens with definitions of the different senses in which things are said to be given. Thus lines, angles, and ratios may be given in magnitude, rectilinear figures may be given in species or given in form, points and lines may be given in position and so on.

These definition are followed by 94 propositions which state that when certain aspects of a figure are given, other aspects are given (Boyer, p. 117-118: Bulmer-Thomas p. 425-430). The Data is also considered important in the development of algebra. (B.L.

Van der Waerden, Science Awakening I, trans. Arnold Dresden (Groningen Holland: P. Noordhoff, [1975?]), p. 198) Ammar: Mr. Euclid, what is your book On Division of Figures based on? Euclid: It consists of 36 propositions concerning division of various figures into two or more equal parts or parts in given ratios. These divisions may be into like figures.

On Division of Figures also contains division into unlike figures. The figures include triangle, parallelogram, trapezia, circles quadrilaterals, and figures bound by an arc of a circle and two straight lines from a given angle. Another important thing that book has is the proofs. Among those proofs only four have survived because the others were proved to be wrong (Bulmer Thomas, p. 426; Heath, Greek, I p. 425-6).

Ammar: I heard a lot about your book Phaenomena. It gained a lot of popularity. Tell us some important points of that book. Euclid: It is a tract on sphaeric, the study of sphaerical geometry for the purpose of explaining planetary motions (Heath, Greek, I p. 11-12).

It is present in Greek and is quite similar to On the Moving Sphere. In the book, I stated that an ellipse may be obtained from cutting a cylinder. Ammar: I heard that your book Optics was much more different than your other books. What are the things that make this book separate from your other books? Euclid: Optics is the earliest surviving Greek treatise on perspective. In this book I followed the Platonic tradition that vision is caused by discrete rays which emanate from the eye because I felt the reason that they stated was mostly similar to the results that I obtained(Bulmer-Thomas, p.

430). Ammar: Some of your works didnt gain that much popularity. Tell us about those works of your that are unknown to us. Euclid: The four works that are very useful but are unknown. They are Conics, Porisms, Pseudaria, and Surface Loci. It is on the same work as of Mr.

Apollonius. Porisms contained 171 theorems and 38 lemmas. About Pseudaria I can only say is that it helps beginners and teaches them that how can they avoid errors in their research. The English name for this book is Book of Fallacies and the name gives an idea that what the book is about. The book Surface Loci is consists of geometry and it gives an overview of almost all the geometrical figures.

Ammar: I have heard a lot about Elements. It would be a pleasure if you would tell us something about the Elements. Euclid: As you know that Elements has 13 Volumes. These volumes are based on different perspectives. They discuss about plane geometry, solid geometry, proportion in general, the properties of numbers, and incommensurable magnitude. Ammar: You did some work in mythology too. What topic is your mythology based on? Euclid: It is based on axioms, definitions, and postulates. Ammar: Would you please explain us something about it.

Euclid: A definition is a statement that requires only an understanding of the terms being used. It says nothing about existence of the thing being defined (Heath, Elements, I, p. 118, 143). An axiom is an exertion, the truth, which is taken for granted as being blatantly obvious, and which is applicable in all sciences. Postulate means to assume without a proofs.

Aristotle gave three ways of differentiating between postulates and axioms. They were: 1. Postulates are not self-evident as are axiom. 2. Postulates are applicable only to the specific science being considered where being axioms are more general. 3.

Postulates assert that some things exists whereas axioms do not. (Heath, Elements, I, p. 117-9). Ammar: In your opinion what is a proposition Sir. Euclid: I think a proposition may be a statement about all the properties of an object.

Euclid: What about you? What do you think about a proposition? Ammar: A proposition could be divided into six formal parts. It could be enunciation, specification, construction, proofs, and conclusion. Ammar: I heard that one of your work lead to an argument. Can you tell us? Euclid: The argument was that all right angles are equal to one another and that is possible to draw a straight line from any point to any other point. You know that by taking that Ptolemy I created a quote that There is no royal road to geometry and later it changed to There is no royal road to learning. Ammar: Your work has been translated to into many different languages. In what language was your work was translated first? Euclid: My work was translated for the first time in Arabic around 1482 AD.

After that it was translated into Latin and then into other European Languages. Ammar: Do you remember any name of the person who translated your work? Euclid: Yes, I remember one guy. His name was Tartaglia and he was Italian. He translated the Elements. Ammar: OK sir, it was a pleasure meeting to you.

Thanks for your interview. Euclid: It was my pleasure to meet you. Bye! Bibliography 1. http://www-groups.dcs.st-and.ac.uk/~history/Mathem aticians/Euclid.html 2. http://www.altavista.com 3. http://stat.tamu.edu/~dcljr/Euclid.html 4. Encarta encyclopedia 98, Keyword Euclid 5. Bookshelf 98, Keyword Euclid 6.

A concise of History of Mathematics, Dark J. Struik. p. 1,44-46,48-50,55-57,59,60,69,72,80,84,102,145,146, 162,167,169,170,173. 7. A history of Mathematics, Carl B.

Boyer. p. 100-119, 51, 53, 66, 79, 89, 120, 122, 141, 145, 151, 158, 164f, 167, 171-173, 178, 184, 189-191, 227, 234, 239, 242, 279f, 263, 304, 319, 391, 437, 443, 459, 468, 482f, 485, 488, 501f, 548, 562, 572, 605, 609, 616, 638. 8. Men of Mathematics, E.

T. Bell. p. 7, 14, 19-20, 27, 75, 127, 153, 165, 176, 215-6, 223, 266, 299-303, 305-306, 314, 351, 358, 379, 399-400, 443, 454, 474, 514. 9.

Instant Physics from Aristotle to Einstein, and Beyond, Tony Rothman. p. 12. 10. Journey through Genius, The Great Theorem of Mathematics, William Dunham. p.

27-83,131. History Reports.