1. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Why we learn Thales’s Theorem Prepared by : Gabriel TAGA Nicolae ANGELESCU Universitatea Spiru Haret ROMANIA

2. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Presentation Outline Thales of Miletus Thales’s Theorem Conclusion

3. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Tell me it is easy!!! But 1/7 = 0,(142857)‏ How can we measure this? It is easy? Thales has the answer. A1 A 2 A 3 A 4 A 5 A7 A 6 1/72/73/74/7 5/7 6/7 7/7 B A

4. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus Born: about 624 BC in Miletus, Asia Minor (now Turkey)‏ Died: about 547 BC in Miletus, Asia Minor (now Turkey)‏ ' The first man in history to whom specific mathematical discoveries have been attributed ' Boyer- A History of Mathematics

5. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus Miletus

6. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales was interested in almost everything, investigating almost all areas of knowledge, philosophy, history, science, mathematics, engineering, geography, and politics. He proposed theories to explain many of the events of nature, the primary substance, the support of the earth, and the cause of change. Thales was much involved in the problems of astronomy and provided a number of explanations of cosmological events which traditionally involved supernatural entities. His questioning approach to the understanding of heavenly phenomena was the beginning of Greek astronomy.

7. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Greek physical philosopher, son of Examyus and Cleobuline,it is universally recog nized as the founder of Greek geometry, astronomy and philosophygeometry astronomy philosophy

8. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus According to Proclus to Thales we owe several propositions later included by Euclid in his Elements (i) A circle is bisected by any diameter. (ii) The base angles of an isosceles triangle are equal. (iii) The angles between two intersecting straight lines are equal. (iv) Two triangles are congruent if they have two angles and one side equal. (v) An angle in a semicircle is a right angle.

9. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 The proposition 2, Book VI of Euclidean Elements3 “If a straight line be drawn parallel to one on the sides of a triangle, it will cut the sides of the triangle proportionally; and, if the sides of a triangle be cut proportionally, the line joining the points of section will be parallel to the remaining side of the triangle ".

10. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus

11. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus measured the heights of pyramids = measuring their shadows

12. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus measured distances of ships from shore = creating a triangle (ΔCDE) similar to triangle ΔABS.

13. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus

14. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Conclusion Being asked what was very difficult, he answered, in a famous aphorism, “To Know Thyself.” Asked what was very easy, he answered, “To give advice.” The achievement of Thales, has been represented by historians in two entirely different lights: on the one hand, as a marvelous anticipation of modern scientific thinking, and on the other as nothing but a transparent rationalization of a myth. What is the fastest? The mind. It travels through everything. Take Home Message:

15. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thank you!

16. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus

17. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus

18. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus

19. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales of Miletus An angle in a semicircle is a right angle.

20. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 L ike the absent minded professor stereotype we know of today, Thales has been described in both glowing and derogatory tales. One story, told by Aristotle, says Thales used his skills to predict that the next season's olive crop would be bountiful. He then purchased all the olive presses and made a fortune when the prediction came true. Plato, on the other hand, told a story of how one night Thales was gazing at the sky as he walked and fell into a ditch. There was a pretty servant girl nearby who came to his rescue, then said to him "How do you expect to understand what is going on up in the sky if you do not even see what is at your feet". Thales of Miletus

21. http://letsdoit.upol.cz/ This project has been funded with support from the European Commission. This courseware reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein Project No. 2009-1-IE1-BRN06-007179 Thales