Mathematics Point as an Example of a Mathematics Museum
Mathematics Point is a museum-like exhibition hall established to make mathematics popular, facilitate understanding, provide information about the historical development of mathematics in our country, to display mathematical objects used in the past such as mechanical calculators and rubu boards, and mathematics books used in the Ottoman Empire by making proofs with hand-held and visible models. It was created as an infrastructure project by Faculty of Science faculty members Mehmet Üreyen, Nevin Mahir, Nezahat Çetin, Bünyamin Demir, Taner Büyükköroğlu, Serkan Ali Düzce and Ali Deniz. The work started in December 2007 and was completed in February 2011. The project was drawn by Füsun Curaoğlu and Çağatay Uğurlu. Models were produced by Anadolu University Workshops and MEB (Ministry of Education) Course Equipment Production Center according to the plans and projects suggested by the project coordinators. Antique books and materials are a personal collection for an indefinite exhibition.
When you enter the hall, you can first see antique books lined up on the opposite shelf. These books are mostly mathematics books used during the Ottoman period. These books are exhibited in order to respectfully commemorate our mathematicians who contributed to the development of mathematics in our country and who wrote these books, to introduce them to the younger generations, and to give an idea about the level of mathematics in our country during their period. Each of these books has a different story. To give a few examples, the famous works of the famous science historian and mathematician Salih Zeki Bey (1864-1921) Âsâr-ı Bâkıye 1, 2 and Kāmûs-ı Riyâziyyât are two examples. While the historical development of trigonometry in the Islamic World is explained in the first volume of Âsâr-ı Bâkıye, and the historical development of algebra in the same period in the second volume, Kāmûs-ı Riyâziyyât is an encyclopedia of mathematics; Salih Zeki Bey could only write the first volume of this work, and he di not live enough to finish his work. It is possible to see works such as Vidinli Hüseyin Tevfik Pasha's (1832-1901) Linear Algebra, in which he created an algebra in three-dimensional space, Kerim Erim's (1894-1952), the first Turkish to have a doctorate in mathematic, analysis books, logarithm tables written in the Ottoman period, Nasıreddin Tusi's (1201-1274) Şeklü'l-ḳaṭṭâ, the Latin original edition of the first analysis book written by the famous mathematician Euler in 1748 and using the word function, the French translation of Euclid's geometry conducted in 1676, 170 original printed works, mostly in Ottoman, such as the geometry book written by Atatürk in which there are Turkish names of some geometric shapes we use today such as triangles and quadrilaterals as well as al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr's, which is accepted as the first book written on algebra in the world by the famous Turkish mathematician Khwarezmi (780-850), facsimile editions in Arabic, English, and Latin, the facsimile printing of Miftah al-Hisab written by Gıyaseddin Cemşid (Al Kaşi) (-1429), which is considered the first book in the world to use decimal numbers, and were used for many years in the Ottoman Empire, and the facsimile printing of the astronomy work titled Risale-i fi'l Fethiye, presented to Fatih by Ali Kuşçu (-1474).
As another group of antiques, many mathematical objects such as rubu board, astrolabe, planimeter, mechanical and electronic calculators, and slide rule can be seen. Mechanical calculators were used before electronic calculators in the 20th century. While only addition and subtraction can be done with hand types, three or four operations can be done with table types. Trigonometric calculations are made with some of them. It was used to determine the positions of celestial bodies, especially in the Islamic world, before the astrolabe telescopes. The planimeter has been used in topography to calculate areas bounded by curves as an application of Green's theorem. The Rubu board was used in the Islamic world from the 12th century to determine prayer and fasting times. Rubu board is prepared according to the latitude and longitude of the region, and it is called rubu in the sense of a quarter because it is in the form of a quarter circle. The elevation angle of the sun is measured with the face of the Rubu board called Mukantarat, and calculations are made with the Rubu'l Müceyyeb face. With this face, sines, and cosines of angles, multiplication, and division of two numbers, square, square root, and cube of a number can be calculated; the cube root of a number can be approximated. As it has been used since the 12th century, it is considered to be the ancestor of calculators. Sliding rulers, on the other hand, are tools that engineers make all kinds of calculations before electronic calculators after the discovery of the logarithm in 1614.
Secondly, the handmade Kütahya tiles on the shelves draw attention. There are 17 of these tiles and there is a deep mathematics behind them, we can explain it roughly like this: The symmetry transformations in the plane are translation, rotation, reflection and shear-reflection symmetries. Wallpaper coverings are first classified according to the smallest angle of rotation of the rotational transformations found between the symmetries of this coating. The angles of rotational symmetries in a wallpaper overlay can only be 60, 90, 120, and 180 degrees or the overlay does not have any rotational symmetry; this angle constraint is called the crystallographic constraint. When wallpaper coverings are classified according to the symmetries they have, only 17 different symmetry groups emerge. These groups are called wallpaper groups. Here, each covering hanging on the wall is an example of one of these groups.
It is possible to see some of these 17 coatings in various historical works in Anatolia, but all together, they are only found in the Al-Hamra palace in Spain in the world; the second one is in this hall, to our knowledge.
At the entrance of the hall, a strange object is seen secondly. If you were to say an object that has only one face, you would probably say that it is impossible since every object has at least two faces. However, the German mathematician Felix Klein showed that it is possible. This strange object you see is a compact one-sided object that we call the Klein Bottle. When you start from one place and finish the painting process to paint only one side of the object, you will see that all sides of the object have been painted; that is, there is no such thing as crossing over to the back side because there is no back side. Similarly, the Möbius strip that you will see a little further on is one-sided, and you can easily see that it is one-sided. After the Klein bottle, a model is seen in which it can be proved that the number Pi is the ratio of the circumference of the circle to its diameter, that this ratio does not change as the circle changes, and that its approximate value is 3.14. When you go a little further, you will see the trigonometry circle by which you can calculate the sine and cosine of an angle without the need for a calculator. You can find the volume formula of a sphere, which can be calculated as a result of long processes with paper and pencil, with the model here, and you can easily prove the Pythagorean theorem with a model here.
In our proof table like these, from the proof of why the area of a triangle is half the product of the base and the height 1/4+(1/4)^2+(1/4)^3+...the infinite sum equals 
1/3, many proofs can be made with models without using pen and paper.
In the shortest time curve model, you can predict which ball will light the lamp first.
Before examining the shelves on the left, you can try to solve the riddles by playing a number game and trying to fill the magic squares.
On the shelves on the left, you can examine five regular polyhedrons, curved surfaces formed by lines, and dozens of object models such as intersections of different objects, and see how these objects were formed. For example, you can see how the object whose base is a circle, whose intersections are equilateral triangles with planes perpendicular to the diameter of the base, or the rotational objects formed by the rotation of a planar region around an axis on the same plane, and example models of the formation of the cones of Apollonius, the Antalya Compass.
The genius of Archimedes (287-212 BC) can be seen in his model of calculating the volume of the sphere.
After seeing dozens of models and proofs, of which we have given a few examples above, the hall tour ends with an example of mathematics in nature with the Fibonacci sequence in sunflower and pine cone.
NOTE: The hall was created when the Faculty of Science was affiliated with Anadolu University. The Faculty of Science was affiliated to Eskişehir Technical University( ESTU) in 2018. For this reason, those who want to see and examine the hall should contact ESTU Social Communication Unit.
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