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mathblag | Musings on mathematics and teaching.

Musings on mathematics and teaching. (by David Radcliffe)

http://mathblag.wordpress.com/

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mathblag | Musings on mathematics and teaching. | mathblag.wordpress.com Reviews
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Musings on mathematics and teaching. (by David Radcliffe)
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mathblag | Musings on mathematics and teaching. | mathblag.wordpress.com Reviews

https://mathblag.wordpress.com

Musings on mathematics and teaching. (by David Radcliffe)

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mathblag.wordpress.com mathblag.wordpress.com
1

Gelfand’s Question | mathblag

https://mathblag.wordpress.com/2013/06/19/gelfands-question

Musings on mathematics and teaching. Gary Davis ( @republicofmath. Has brought my attention to a question. That has been attributed to Israel Gelfand: What are the possible sequences of leftmost digits of 2. For example, when n = 2 the sequence of powers is 4, 9, 16, 25, 36, 49, 64, 81. And the sequence of leftmost digits is 4, 9, 1, 2, 3, 4, 6, 8. The leading digit of k. Log(4) = 2 * log(2). Log(5) = 1 – log(2). Log(6) = log(2) log(3). Log(8) = 3 * log(2). Log(9) = 2 * log(3). Then a = b = c = d = 0.

2

July | 2013 | mathblag

https://mathblag.wordpress.com/2013/07

Musings on mathematics and teaching. Month: July, 2013. July 15, 2013. A Generalization of the Birthday Problem. In a group of. People, chosen at random, what is the probability that two or more share the same birthday? We assume that birthdays are distributed equally among the 365 days of the year, ignoring leap days. This question is known as the Birthday Problem. Which was published in the New York Times. A more advanced treatment can be found in Wikipedia. Explaining Huffman’s Impossible Pyramid.

3

Explaining Huffman’s Impossible Pyramid | mathblag

https://mathblag.wordpress.com/2015/03/11/explaining-huffmans-impossible-pyramid

Musings on mathematics and teaching. Explaining Huffman’s Impossible Pyramid. I read about Huffman’s Pyramid from the consistently excellent blog Futility Closet. Huffman’s Pyramid is a drawing of a figure that cannot exist. However, the impossibility of this figure is hardly obvious. Here is the reason: if the slanting lines were extended, then they would have to meet at the apex of a pyramid. However, the lines do not meet. Contradiction! Are you convinced yet? To represent a polyhedron with two triang...

4

Fibonacci Pigeons | mathblag

https://mathblag.wordpress.com/2011/11/14/fibonacci-pigeons

Musings on mathematics and teaching. Here is a funny picture that has been circulating the Internet since September 2010. I think that analyzing this picture would be an interesting project for a high school math class. My own analysis is included below. This picture is amusing, but I wondered if it was real. Some people claim that the picture was Photoshopped. I don’t know how to tell if it was faked, but I do know how to count pixels. The fit is good, but not spectacular (R. Conclusion: the picture is ...

5

Inscribed polygons and the Fourier transform | mathblag

https://mathblag.wordpress.com/2013/10/08/inscribed-polygons-and-the-fourier-transform

Musings on mathematics and teaching. Inscribed polygons and the Fourier transform. Draw a polygon in the plane. We can construct a new polygon by connecting the midpoints of the original polygon. I will call this the. What happens if we repeat this process many times? Ie a regular polygon to which a linear transformation has been applied. Since linear transformations carry circles to ellipses, it follows that the limiting shape can be inscribed in an ellipse. By Isaac J. Schoenberg. Be a fixed integer&#4...

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blog.republicofmath.com blog.republicofmath.com

When is an integral not an integral? | Republic of Mathematics blog

http://www.blog.republicofmath.com/when-is-an-integral-not-an-integral

Republic of Mathematics blog. Republic of Mathematics Home. When is an integral not an integral? September 14, 2013. By Gary Ernest Davis. No surprise to anyone really that students get confused by the difference between definite and indefinite integrals. The so-called indefinite integral is not really an integral at all, not in the sense of area: it’s the solution set to a differential equation. It’s not even usually a single function at all, but a whole family of functions. As is commonly written.

ajk44.wordpress.com ajk44.wordpress.com

Conventional Wisdom | Alison Kiddle's NRICH blog

https://ajk44.wordpress.com/2011/11/10/conventional-wisdom

Alison Kiddle's NRICH blog. Thoughts about maths, education, and working for NRICH. ICT in the Classroom. There are some truths in mathematics that are true because they are true because they are true. For example, if I have a right-angled triangle in the plane, the square on the hypotenuse has to be equal to the sum of the squares on the other two sides. Other truths are true in a different way. It’s true to say that this:. But despite my strong feeling that it is the necessary truths that are core to m...

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mathblag | Musings on mathematics and teaching.

Musings on mathematics and teaching. March 11, 2015. Explaining Huffman’s Impossible Pyramid. I read about Huffman’s Pyramid from the consistently excellent blog Futility Closet. Huffman’s Pyramid is a drawing of a figure that cannot exist. However, the impossibility of this figure is hardly obvious. Here is the reason: if the slanting lines were extended, then they would have to meet at the apex of a pyramid. However, the lines do not meet. Contradiction! Are you convinced yet? To represent a polyhedron...

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mathblatz – Seven Sparks from the Seventh Son

Seven Sparks from the Seventh Son. August 15, 2016. Seven Sparks from the Seventh Son. Zero in on Your Values. Start with a master list-. This part was pretty easy thanks to John Manning’s list on pg. 43 of. I felt the list was a great summary of a lot of the values I feel are a part of me. Then the hard part Zero in -Identify your core values-. I feel this is the most important value for me because I truly feel if you are not truthful nothing else matters. Compassion for all lives-. As I finished this I...