MATHEMATICAL MINIATURES 66

Discover the world of mathematics in a fascinating way! The "Mathematical Miniatures 66" volume is a collection of three miniatures aimed at students in the seventh and eighth grades of primary schools. Prepared by members of the Organizing Committee of the Kangaroo Mathematical Competition, this volume is ideal for both students and teachers looking for inspiration and materials for working with young people. You will find issues related to angle bisectors, irrational numbers and number sequences.

• Inspiration for students and teachers
• Issues from geometry and algebra
• Accessible language for young people
• Tasks for self-solution
• Prepared by experts from the Kangaroo Mathematical Competition
• Ideal material for working with young people

This volume, published in the year of the centenary of the Polish Mathematical Society, contains articles inspired by tasks from the Task League and the style of Stefan Banach's textbook. The first miniature concerns the properties of angle bisectors of internal and external angles of various polygons, focusing on the formation and shape of a polygon whose vertices were formed by the intersection points of the angle bisectors. At the end of the article there is a series of tasks for self-solution, which allows you to consolidate knowledge and develop mathematical skills.

The second miniature is inspired by the style of the algebra school textbook by Stefan Banach, a symbol of Polish mathematics. This article contains arithmetic considerations regarding irrational numbers, in particular it gives various meanings of the word "root" and an algebraic definition of the root of a number as a solution to a certain equation. The discovery of the number root of two has its roots in the geometric issue of the mutual relation between the side length of a square and the length of its diagonal.

In addition, in the article we will find a sketch of the construction of a power with a rational exponent, a few words about rounding and some historical information related to the presented topic. The aim of the third miniature is to familiarize the reader with the concept of a number sequence, in particular described recursively. To illustrate the presented content, the most well-known irrational numbers were used, i.e. the square root of two and ?. Using these examples, it is shown how to locate irrational numbers on the number axis by constructing a sequence of approximations. Then the author shows the role of the concept of the sequence in the definition of the golden number and its application in the interpretation of combinatorial problems. The Mathematical Miniatures 66 volume is an excellent way to develop mathematical interests and deepen knowledge in the field of geometry and algebra. We wish you a pleasant reading and fruitful work!