asymptotes

People tend to think that exams would be much easier if they're in multiple-choice format. But does having more choices really make them easier? Consider the test item below: Who among the following scientists contributed to the atomic theory? A.) John Dalton B.) Charles Darwin C.) J.J.Thompson D.) Albert Einstein ... ... ... S.) All of the above T.) All letters above that are valid Roman Numerals U.) All letters above that correspond to a Fibonacci number V.) All letters above which are valid symbols of an element in the periodic table W.) All letters above which are elements of the union of the sets in U and V X.) All letters above which are elements of the intersect of the sets in V and W Y.) None of the above Z.) Sirit (Filipino word for ¨I give up¨)   Post Script A few lessons we can gather from the above post: * Having a lot of choices may not be good all the time. * No matter how many choices you have, you always have to choose the right one. * ...

The poem that follows is a tribute to Euler's magnificent observation that : Euler's Irrational Imagining i to the i you equal, do you not, one over the square root of e to the pi ? What is interesting about the above equation is the fact that it involves 3 of the most important numbers in Math: the imaginary number i , and the irrational numbers e (Euler's number) and pi . Morover, it shows that an imaginary number raised to an imaginary number could actually result in a real number! Contemplating this equation, one could not but appreciate the inherent beauty that exists in math. Sidelight   I consulted a professor one time.  We discussed the graph output of the results of my experiments.  After staring at the graph for a couple of seconds, he suddenly smiled and said "It's beautiful, isn't it?" Of course, I could not disagree, lest he gives me a failing mark. So I just parrot him and said "Uhmm..ah...yes... it...

Note: You need to know Tagalog/Filipino to appreciate this proof.  Problem: Prove the following: log 2   = z   n Proof Expanding the Left Hand Side of the equation: log two = z n Substituting phonetically log tu = z n Expanding the Right Hand Side of the equation... log tu = zzzzzzz.... Using the commutative property: tu log = zzzzzzz.... Q.E.D.

It's been more than ten years since I took up differential and integral calculus (more familiarly known as Math 54) during my college days in UP Diliman. I've long forgotten most of the formulas and techniques I learned then, but the memory of the person who taught them to me remains vivid. She was Ma’am K. The first thing that struck me about Ma'am K was her mastery of the subject she was teaching. She would explain things with conviction and authority, even reciting long theorems from memory. She also remained focused on the exposition of the lesson. Once, while teaching, the chalk fell off her hand, but she continued with the discussion even as she was picking it up from the floor. Later on, it became obvious to me that she possessed an extraordinary intelligence. But Ma’am K was not just an intelligent instructor, she was also a competent one. I've met some very intelligent professors in U.P., but many of them, sad to say, do not know how to teach. They s...

Funny how we find it heroic and admirable when one disciplines his body in order to be a good athlete or a good soldier and yet we find it absurd when we’re told that we have to discipline our body in order to be a good Christian.   Funny how we find it right and just that a person pay for his offenses and yet we find it crazy when we’re told we have to atone for our offenses against God. Funny how we find it romantic and poetic when a human lover suffers with and for the sake of his Beloved and yet we find it stupid when we’re told that we have to suffer with Christ. [1] Suffering is present in all three cases mentioned above; but suffering is not what is sought, but dominion , atonement , union .   Dominion over our passions, atonement for our sins and union with Christ: these are some reasons why the Church prescribes sacrifice and self-denial, most especially during the seasons of Lent and Advent.  --- NOTES Death of Turin Turambar from aryundomiel....

We don't have to go through life without a map. Many people have already gone to where we ought to go; we just have to follow their lead. These people have left us maps for understanding the terrain, showing us where the true path lies and where to expect dangers. I am, of course, referring to books on how to live life to the full. In this article, I have provided a shortlist of books I recommend for understanding and living better life in general and the Christian Life in particular. Basic Catholic Doctrine Books for systematically studying the Catholic faith; good reference materials for consulting articles of faith The Faith Explained by Leo Trese Compendium of the Catechism of the Catholic Church The Catechism of the Catholic Church Living the Faith Books that give insights and suggestions on how to live the demands of the faith according to one's circumstance. Also useful for spiritual reading. Jesus as Friend  by Francisco Fernandez-Carvajal Friends of Go...

Download a PDF copy of this article   I.Introduction All men desire peace and happiness, but many do not realize that true peace and happiness could come in a box- in a confessional box that is. Many Catholics neglect, delay or fear going to confession for various reasons. In this article, I will try to answer common objections on why one needs to go to confession and why one needs to go soon. I neither presume that I have covered all possible questions and objections about going to confession, nor that I have answered completely the questions I have posed. I am convinced that, more than rational arguments, what are needed for conversion are the grace of God and the person’s humility, faith and trust. Nevertheless, I still dare to tackle these questions in the slightest hope that even just one reader decide to avail of this great sacrament and enjoy the presence of God at the center of his soul. II.Objections to Confession Going to confession for the first time, o...