Category: Uncategorized
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My annual stint of grading IB papers started this week. So I will tackle only a relatively simple problem today. I will take a break for about three weeks while I am grading papers and resume after that. I recently came across the problem depicted below. We are given that the external quadrilateral is a…
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There are many ill-informed ideas about mathematics. One is that there is a solution to every problem, as suggested by the meme above. This is not true. There are problems that have no solutions. Then there are problems which have solutions, but whose solutions cannot be solved without significant computational power. And there are problems…
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This will be the final post in the series on counting principles. Here, I wish to deal with a strange idea of balancing parentheses. If that seems like a strange term itself, let me explain. An arrangement of n left parentheses ‘(‘ and n right parentheses ‘)’ is said to be balanced if, for every…
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Launching Pad We are in the middle of a series on counting principles. In The Inclusion-Exclusion Principle, we saw a method of counting that ensured we counted everything while not double counting anything. Now, we are ready to go ahead with our study of derangements as promised. Understanding Derangements Let us first define what a…
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Recapitulation We are currently in the middle of a series on counting principles. At the conclusion of the previous post, I had promised you that we would look at the idea of derangements. However, I realized that we need to lay some ground work before we get to derangements. When we count, how do we ensure…
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After an extended break for Lent, we continue with the series on counting principles. I had ended the last post in the series with a promise that we will look into the technique of partitioning. And I had left you with a problem to solve: Given that x, y, and z are natural numbers, how many solutions exist to…
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As mentioned earlier, I am taking a break from publishing new material for a few weeks. During these weeks I am republishing the series on e and the one on π. The post below was originally published on 20 September 2024. I will resume with the series on counting principles next Friday. Coming Back Full…
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As mentioned earlier, I am taking a break from publishing new material for a few weeks. During these weeks I am republishing the series on e and the one on π. The post below was originally published on 6 September 2024. Coming Back Half Circle We are in the middle of a series of posts…
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As mentioned earlier, I am taking a break from publishing new material for a few weeks. During these weeks I am republishing the series on e and the one on π. The post below was originally published on 16 August 2024. A Slice of the Pi We are in the middle of a study of…
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As mentioned earlier, I am taking a break from publishing new material for a few weeks. During these weeks I am republishing the series on e and the one on π. The post below was originally published on 9 August 2024. Definitionally Limited Almost everyone who has studied beyond Grade 4 has probably heard of…
Acutely Obtuse 