THE MATH AND SCIENCE JOURNAL
The Guivy Zaldastanishvili American Academy in Tbilisi
Latest Articles
Unsolved Problems in Mathematics
by Ninia Dzneladze, Kato Rcheulishvili, Elene Mansvetashvili
Teacher: David Shapakidze
A few of the unsolved math problems are considered below. Although there are many of
them, the article only talks about two, the Collatz Conjecture and the Magic Square of Squares.
The third one, Fermat’s last theorem, is also included, although it is proven to have an
explanation. However, the problem took a very long time to be cracked and it changed
mathematics, so it is an important equation, left unsolved for many years. The examples
examined aren't the solutions to any of the problems, but can help understand the concept better.
Math Project
Sphere Eversion
by Barbare Motsonelidze, Nini Tcharbadze and Anna Kirvalidze
Teacher: David Shapakidze
In 1957 two brilliant mathematicians and topology experts Steve Smale and
William Thurston presented a revolutionary idea which to an inexperienced person might
seem impossible. Their discovery is known under the name of Sphere Eversion, and gives
proof of how a sphere is able to turn inside out.
Zeno’s Paradoxes of Motion: The Unification of Philosophy and Mathematics
by Lile Tsitskishvili, Mariam Kvaratskhelia, Tamar Akhobadze
Teacher: David Shapakidze
This article discusses Zeno’s famous motion paradoxes: Achilles and the Tortoise, the dichotomy, the moving rows, and the moving arrow paradox. The mentioned have one thing in common, all question the reality of elementary notions, such as the existence of motion and time,
and try to challenge the accepted ideas in both mathematics and everyday life. These puzzles open up the narrow-minded vision of anyone who decides to explore it in depth. Although these
paradoxes are mind-blowing suggestions introduced by Zeno, they unify philosophy and logic that is impossible to disprove without an understanding of mathematics. The article will provide a mathematical and physical analysis using geometric sequences, the infinity concept, and movement to disprove the controversial proposals which have confused great minds forcenturies.
Robotics: Industrial Robotic Arm
by Dachi Gvinadze
The article introduces the principles of robotics and the factors that determine
functionality, efficiency, and cost. The purpose of the article is to explain the basics of industrial robotic arms and the science behind them. The topics explained in the paper are: “The Mechanics”; “The Electronics”; and “The
Choices of Material”; These topics are discussed in depth to understand what makes an industrial robotic arm efficient, cheap, and functional for the given needs. The article also briefly overviews the different types of industrial robots.
Geometric Tessellations in Architecture
by Nikoloz Lobzhanidze, Irina Panjavidze
Teacher: Lasha Kokilashvili
Patterns are integral part of our life. We observe them in everyday life: nature, art, architecture, etc. A tiling or tessellation is the covering of a surface using one or more geometric shapes, with no overlaps. Any type of a repeating pattern that can be observed in real life, like carpets, rugs, wallpapers can be identified as being one of 17 distinct symmetry groups. Being an important area of mathematics, tessellations play a significant role in architectural design, both two dimensional as well as three dimensional. This paper discusses the brief history of tessellations, application in modern architecture, mathematics behind and presents several case studies relating to the illustration of application of tessellations in tiling as well as astonishing examples found in a number of locations in the Tbilisi Academy of Fine Arts.
Enigma of the Night Sky
by Lizi Ebralidze
To answer the simple question, "why is the night sky dark?" we dive deep into the core of modern cosmology. For ancient astronomers, an assumption of an infinite, static universe conflicted with the night sky's darkness. However, today this question is no longer paradoxical because fundamental aspects of modern-day cosmology can explain it. Heinrich Olbers, a person who formally addressed this paradox, used the concept of absorption to explain his paradox, but the zeroth law of thermodynamics disapproves of his explanation. The age of the universe and the finite speed of light enables us to conclude that the stars have not been shining forever, some of their light has not even reached us yet, and therefore night sky should not be bright. Another explanation concerns the nature of light- its ability to stretch over long distances and form infrared waves (one of the invisible electromagnetic radiations), making distant stars invisible to the observers on Earth.
Acknowledgements
Special thanks to the following field professionals for their invaluable advice to the students:
Ketevan Sturua
Nino Mitsishvili
Mariam Toradze
Tamaz Vasadze
David Shapakidze