Posted in Beautiful math, geometry by: admin
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23 May
The problem is credited to V. V. Proizvolov and may serve an example where using dynamical software to sketch a diagram proves to be a distraction. I put together a GeoGebra applet and looked at the possible properties of the configuration with several elements added. Meanwhile, Hubert Shutrick pointed out its obvious, salient feature. The solution is a one liner
Posted in Beautiful math, geometry, Simple math, Uncategorized by: admin
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11 Sep
This remark helps solved the following problem: in the diagram below, sum the areas of the circles in the two squares; which is larger: the sum of the two areas on the left or that of the four circles on the right? Or, may they per chance be equal?
Posted in Arithmetic, Beautiful math, Early math, Homeschooling, Uncategorized by: admin
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21 May
Parity is the simplest mathematical concept after counting. 1 is an odd number, 2 is even, and then they come intermittently: 3, 5, 7, ... are odd, 4, 6, 8, ... are even. A pile of an even (but not odd) number of items can be divided into two piles of equal sizes. An odd [...]
Posted in A must read, A must see, Beautiful math by: admin
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05 Apr
After a hiatus of several month, Carnival of Mathematics is back online. Do check the revived carnival at The Aperiodical page by Peter Rowlett, Katie Steckles, and Christian Perfect. The new edition is both edifying and entertaining.
Posted in Algebra, Beautiful math, Simple math by: admin
7 Comments
24 Feb
In a recent blog A Lovely Observation Gary Davis (@RepublicOfMath) elaborated on an observation of Ben Vitale (@BenVitale) to the effect that In the fractions both numerators and denominators are sums of successive odd numbers: the numerators start with 1, the denominators where the numerators leave off. Thus naturally derivation of the formula for the [...]
Posted in Beautiful math, Early math, Simple math by: admin
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11 Nov
The Extreme Principle The Extreme Principle is a misnamed problem-solving tactic akin to the Worst-Case Scenario often used in combinatorics and computer science. It does not make any claim (like, say, the Pigeonhole Principle) per se, but only suggests that, for some problems, looking into extreme circumstances or elements within the conditions of the problem [...]
Posted in Beautiful math, geometry by: admin
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11 Nov
There are mathematical statements that appear counterintuitive. For example, when it comes to infinities, counterintuitive statements are abundant. At the other extreme, there are statements intuitively obvious that are rather hard to prove. Such, for example, is the famous Jordan Curve Theorem. Naturally, mathematics does not lack in statements of any intermediate kind. Here is [...]
Posted in Beautiful math, Books to read, Graph theory, Homeschooling by: admin
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31 Oct
Many book authors end their book Introduction expressing the hope that readers will enjoy reading the book as much as the author(s) enjoyed writing it. Persi Diaconis and Ron Graham do not. Nonetheless, their book - Magical Mathematics - oozes their enjoyment at writing it. The authors are master storytellers. Movingly, Martin Gardner wrote Foreword [...]
Posted in Beautiful math, geometry, Uncategorized by: admin
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25 Oct
This is a beautiful pieces by Andy Liu, University of Alberta, from the College Mathematics Journal, Volume 42, Number 5, November 2011, p. 372 Parallel lines are usually defined as lines with no points in common. Parallelism is clearly symmetric. If line 1 has no points in common with line 2, then line 2 also [...]
Posted in Arithmetic, Beautiful math, geometry, Simple math by: admin
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22 Oct
Parabola has an easily verifiable property. The segment joining points and crosses -axis in point . The equation of the segment is , from which . This may be a curious fact in its own right. What does it say? Taken at a face value, it simply shows a way to obtain the product of [...]