IITPAL

  Someone very rightly said: “God made the integers, every other number is  that the  work of  man. Now after more  than a century, no mathematician would deny the importance and utility of the developments that Kronecker railed against. Yet  I think  that a lot of  harbors some sympathy for his statement.  The integers hold a special place  within the  heart  of mathematicians.  Many of  the foremost  famous unsolved conjectures relate to the properties of the primes. More importantly, the integers are where we start mathematics: they are how we count.

   लंदन   में   रामानुजन जब सुपर जीनियस भारतीय गणितज्ञ श्रीनिवासन रामानुजन लंदन पहुंचे , तो उनका स्वागत प्रोफेसर गॉडफ्रे हेरोल्ड हार्डी ने किया। बर्फ को तोड़ने के लिए , हार्डी ने एक निर्दोष टिप्पणी की कि टैक्सी की संख्या , वह 1729 में आया था - एक उबाऊ संख्या की तरह लग रहा है , सामान्य अंग्रेजी मौसम के बजाय एक बातचीत शुरू करने के लिए।   रामानुजन की टैक्सी नंबर प्लेट पर एक सरसरी निगाह थी और उन्होंने घुटने की तरह से लापरवाही से जवाब दिया " ओह नहीं , वास्तव में यह एक बहुत ही रोचक संख्या है। यह दो अलग - अलग तरीकों से दो क्यूब्स के योग के रूप में सबसे छोटी प्राकृतिक संख्या है। "   और फिर इस प्रतिभाशाली व्यक्ति ने मौके पर समीकरण को बताया पिछले 2000 वर्षों में , इस ग्रह पर केवल दो इंडिगो बच्चे हुए हैं , जिनमें भग्न दिमाग फ्रैक्टल कॉस्मॉस से जुड़ा है - एक श्रीनिवास रामानुजन और दूसरा निकोला टेस्ला है। दोनों नस्लवादी निहित स्वार्...

  When math is taught like other subjects it becomes boring. Mathematics is not a subject of only information's. Its more like a gym, where you build your brains muscles. Without doing how can we build our body. Same way we have to see mathematics. Mathematics is best learnt by doing.  Math is fun. What all we need is enjoy doing it. Mathematics models help us build thinking mathematically.  Graph of mathematical functions are one such aspects which gives lot of insights of functions, trigonometric functions, linear functions and quadratic polynomials are among very popular functions often used in mathematics.  Look below a fun animation mathematical dance.

  Rope around The Earth: Wrap a thread tightly around the earth (along the equator). Now add an extra 2 meters of thread to this length and then wrap the new thread again around the earth in the same circular path (i.e. along the equator).                                                             (Image: Binding rope around the Earth) Now, how high do you think will the thread rise above from the ground ?(Or in other words, what will be the new radius corresponding to this new circumference?) Well, practically one might think that an addition of 2 meter won't make any difference since its too small compared to the size of the earth (which is ~6371000 meters in radius!). And even if it does, the difference will be so small (may be in millimeters or so) that it can easily be neglected? Well, le...

Billiard ball problem can be seen as one elegant mathematical problem. In this article, we will analyse it mathematically. Before we begin, let us first see the problem. Given below is the situation. Can you predict, in which pocket will the ball falls in? Let us now connect this problem with mathematical conditioning. We all know reflection property very well. Now what you have thought is that whenever ball strikes any mirror then it enters into a rectangle which is just a mirror image of it. Now just keep on constructing rectangles with taking common sides CD and BC (initially) then their reflections too. Remember one thing that the ball will keep on moving in its direction until it reaches one of the vertices of our apparent rectangles. and hence it is obvious that the no. of such apparent rectangles that you will need in the horizontal direction will be 67 and in the vertical direction is 100 (smallest possible). being 67 odd hence, it is obvious that it will fall eit...

Ramanujam (The man Who Knew Infinity) The great Indian Mathemagician Shrinivasan Ramanujam never had any close friends and someone asked him the reason. He replied, “ I always wanted to have a good friend, but unfortunately I am not getting anyone matching my expectations” . The man asked what your expectation? Ramanujam replied,  “The numbers 284 and 220 are exemplary friends and I wish is to have that kind of friendship with someone” The man got confused and asked, “How do this friendship and these two numbers connect?” Ramanujam clarified and asked the man to find all the proper Divisors of these two numbers. After a little difficulty, the person listed the divisors:- Proper Divisors of 284 including 1 are 1, 2, 4, 71, 142. and proper Divisors of 220 including 1 are: 1, 2, 4 ,5, 10, 11, 20, 22, 44, 55, 110. Ramanujam asked him to calculate the total of these divisors for each number. The friend did that and the answer was surprising, he got :- 1 +2+ 4+ 71+ 142 = 220 and 1+ 2 +4+...