Enigmatic

  Puzzle to puzzle you "The art of simplicity is a puzzle of complexity."- Douglas Horton   ..... 2. I am the only four digit number such that my square is an eight digit number whose last four digits are myself. Who am I?   3. There are 3 boxes in front of you. One box contains only apples. One contains only oranges and the other contains apples and oranges. And each box is labeled. But the labeling machine out of some fault, labeled all the boxes incorrectly. You can take only one of the fruits from only one of the boxes. How could you label all the boxes CORRECTLY? 4. A frog is at the bottom of a 10-foot well. Each day, it jumps up 3 feet and slips back 2 feet. How many days will it take the frog to escape the well? 5.   If 1=3, 2=3, 3=5, 4=4, 5=4, then, 6=? 6. There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket? Send email to  enigmaticray...

  T echnology with Mathematics                   Nowadays technology spreads its wings all through every sector in life. Proficiency in latest technology becomes inevitable to sustain ourselves in competitive world. We need to update and refresh ourselves with our existing with our existing knowledge and current technology so that we could meet the demand of current and future generation.             Mathematical softwares are abundant today to visualize the concepts which are much complicated when we approach them traditionally with paper and pencil. This article aims at introducing one such existing software which finds useful to educate mathematical students with clear concepts.*             GeoGebra – as the name indicates, it is a dynamic mathematical software that joins geometry, algebr...

Applications of eigen values and eigen vectors                Eigenvalues and eigenvectors play a crucial role in a wide range of applications across engineering and science. Fields like control theory, vibration analysis, electric circuits, advanced dynamics, and quantum mechanics frequently rely on these concepts. One key application involves transforming matrices into diagonal form, a process that simplifies complex calculations.  ...... Practical Applications (i)                  Most structures from buildings to bridges have a natural frequency of vibration. It means all these structures have their own system of eigen vibrations and eigen frequencies. Now external forces like wind and earthquake may cause these structures to undergo vibrations. In case the frequency of these vibrations becomes equal to the natural frequencies of these struct...

  Know Mathematics through Mathematicians  Indian Mathematician – Bhaskaracharya II   Bhaskara II  (1114 – 1185), also known as Bhaskara II and Bhaskara Achārya ("Bhaskara the teacher"), was an Indian mathematician and astronomer.Bhaskaracharya was the first mathematician to write a work with full and systematic use of the decimal number system. Bhaskara II became the head of the astronomical observatory at Ujjain to join Ujjain, India’s “most prestigious mathematical centre” at the time. It was at Ujjain where Bhaskara II would formulate the ideas which would go on to become his legacy. Work of Bhaskara II Bhaskara is mainly remembered for his 1150 A. D. masterpiece, the Siddhanta Siromani (Crown of Treatises) which he wrote at the age of 36. The treatise comprises 1450 verses which have four segments. Each segment of the book focuses on a separate field of astronomy and mathematics. His poem: A fifth part o...

  Vedic geometry A salute to Indian Mathematics   தாய் அவள் போல் ஒரு ஜீவனில்லை அவள் காலடி போல் சொர்க்கம் வேறு இல்லை தாய் மண்ணை போல் ஒரு பூமி இல்லை பாரதம் எங்களின் சுவாசமே                India stands as an epitome in contributing rich values, ethics, knowledge to the entire world all through the ages. Mathematics is a branch of wisdom which ancient Indian people practiced in a well-structured and developed manner. Indians gave the world ‘ZERO’. The mathematical achievements of ancient India remains hidden, but they are coming to the surface in recent times. Now – a – days many books have been written about the advanced mathematics practices in India, including trigonometry and calculus which reached Europe in the Middle Ages through the Arabs.  1. Drawing East West line ·          A stick is fixed and a thin rope of length equal to the stick is fas...

                                                                         Magical 247 ‘A tribute to mother tongue’ - தமிழ்   தமிழுக்கும் அமுதென்று பேர் - அந்தத் தமிழ் இன்பத் தமிழ்எங்கள் உயிருக்கு நேர்                        Tamil, an ancient language has many fascinating features. Here we present one such mathematical beauty of our mother tongue. The number of alphabets in Tamil counts up to 247. Normally we remember 247 with a pattern “ உயிரும் மெய்யும் உயிர்மெய்யும் ஆயுதமும் ”.                       Now mathematically if a denotes the number of vowels( உயிர் ) and b denotes the num...