Category: Uncategorized
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The past week got quite busy all of a sudden and the week ahead also looks like it will be the same. I know I’m in the middle of a series of post on π. I will continue with the series in a couple of weeks. For now, I leave you with some collections of…
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The Growing Frustration It’s frustrating. Yes, you heard me right. It’s frustrating. You may be wondering why I am saying this and in what context. So here goes. Just the other day, I was looking up some perspectives on a mathematics discussion forum. Quite naturally, there were many mathematics teachers in the forum. And quite…
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Setting the Stage I have long been fascinated by patterns that exist in numerical sequences. Early exploration led me to the discovery of the Fibonacci series and the associated Golden Ratio. I also came across Pascal’s Triangle, which remains a source of intrigue. Hence, when I was introduced to the tests for divisibility, I devoured…
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In the last three posts, we have been dealing with some issues related to counting. In Learning to Count, I introduced us to the area of combinatorics and specifically combinatorial arguments. In the second post, Abjuring Double Counting, we looked at the inclusion-exclusion principle that is used to ensure that every element is counted exactly…
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Recapitulation on Counting In the previous two posts, I introduced ideas related to counting. In Learning to Count we introduced the idea of combinatorial arguments, which allowed us to gain some insight on the process of selection. In Abjuring Double Counting we saw the recursive process used to ensure that, when we count members of…
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Recapitulation In the previous post, we had looked at the basic principles of making combinatorial arguments. We saw that these arguments, while deficient in that they do not yield any numerical values, give us insights about how we can count ways of doing a task. In the conclusion of that post, I introduced the idea…
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Background I have been teaching high school students for a while now. While I have taught physics and theory of knowledge, my main focus has been mathematics. One of the more fascinating areas of the high school mathematics syllabus is probability and statistics. Now don’t get me wrong. I know that, in an earlier post,…
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Opening Disclaimer In the graphs below, I have used the data from the relevant sources and may or may not have performed simple mathematical operations (addition, subtraction, multiplication, or division) on the data. The purpose of this is to obscure the factor being discussed, before revealing it, while ensuring that the essential shape of the…
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Grasping for the Absurd Anyone who has studied mathematics till at least the middle school will know that there are certain mathematical ‘artifacts’ called ‘proofs’. Whether we understand them or not, proofs form one of the foundational structures of mathematics, allowing us to take one idea and extend it logically in a variety of directions…
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Fractions and the Loss of Information In my previous post, I had looked at what is gained and more importantly what is lost as we expand the set of numbers we work with. The discussion in that post centered around the closure property of sets of numbers with respect to various mathematical operations. We saw…
Acutely Obtuse 