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Math and Geometry Tools

Research Papers

2021-2022

Unsolved Problems in Mathematics

Authors: Ninia Dzneladze, Kato Rcheulishvili, Elene Mansvetashvili

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. 

Zeno’s Paradoxes of Motion: The Unification of Philosophy and Mathematics

Authors: Lile Tsitskishvili, Mariam Kvaratskhelia, Tamar Akhobadze

This paper 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. 

Geometric Tessellations in Architecture

Authors: Nikoloz Lobzhanidze, Irina Panjavidze

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.

Sphere Eversion

Authors: Barbare Motsonelidze,  Nini

Tcharbadze, Anna Kirvalidze 

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.

Robotics: Industrial Robotic Arm

Author: 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”; 

Enigma of the Night Sky

Author: 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. 

2020-2021

Paradoxes and Infinite Sets

Authors: Dachi Gvinadze, Levan Gogichaishvili, Damiane Kapanadze

The article discusses the paradoxes that could arise due to the superficial and unilateral consideration of the infinity mathematical sets. The list of paradoxes which are discussed in this article is: “Zeno’s paradoxes”, “Ant on a rubber rope paradox”, “Grandi’s series paradox”, and “Hilbert’s paradox of the grand hotel”. 

Greco-Aramaic Origins of Georgian Asomtavruli Script
ქართული ასომთავრული დამწერლობის ბერძნულ-არამეული საფუძვლები

Author: Alexandre Tavberidze

There are many assumptions about the origin of the Georgian Asomtavruli script. According to one of the hypotheses, the creation of the ancient Georgian script is connected with the Christianization of the Kingdom of Iberia, or Kartli. This article discusses two key considerations related to this theory; Namely, the Greek theory, according to which, we should look for the beginnings of the Georgian alphabet in the Greek alphabet.

ქართული ასომთავრული დამწერლობის წარმოშობის შესახებ მრავალი ვარაუდი არსებობს. ერთ-ერთი ვარაუდის თანახმად, უძველესი ქართული დამწერლობის შექმნა იბერიის, ანუ ქართლის, სამეფოს გაქრისტიანებას უკავშირდება. ამ სტატიაში განხილულია სწორედ ამ თეორიასთან დაკავშირებული ორი ძირითადი მოსაზრება; სახელდობრ, ბერძნული თეორია, რომლის თანახმადაც, ქართული დამწერლობის საწყისები ბერძნულ ანბანში უნდა ვეძებოთ.

Quantum Computing and the Future of Encryption

Authors: Salome Mosiashvili, Giorgi Nikvashvili 

Nature’s Favorite Shape - The Hexagon

   This article will discuss encryption in the context of quantum computing. Specifically, it will discuss the significance of encryption and will discuss the phenomena behind quantum computing, attempting to highlight the superiority of quantum computers when it comes to prime factorization. For this, it will explain Shor’s algorithm and assess its significance. It will also touch on quantum cryptography, specifically the BB84 quantum key distribution protocol. Finally, the article will discuss the advantages and disadvantages of quantum encryption protocols and the difficulty behind their real-world implementation.

Authors: Nini Tcharbadze, Anastasia Chioreli 

Hexagons are used by bees to build their beehive and are favored by nature because constructing them requires minimal effort and has maximum outcomes. Hexagons can fill a surface without leaving spaces between itself and its neighboring hexagons.

The Guivy Zaldastanishvili American Academy in Tbilisi

LET’S CONNECT

7a Leo Kvatchadze Str. 

Tbilisi, Georgia

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