2014-02-18 21:14
As I aforementioned, there is a fine line between axiom and definition. In my Holt geometry book there is an axiom that states, if two points are on a plane then the line containing th… Read More
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2014-02-18 21:06
The fifth proposition in the elements is the proves that the angles opposite the congruent sides in an isosceles triangle are congruent. Euclid proves this by extending the congruent sides o… Read More
2014-02-16 17:49
Currently I am planning on reading approximately 10 propositions per week and finish book 1 in a little over a month before going on to 2nd book of the Elements. So today I wanted to begin d… Read More
2014-02-12 06:32
I have just started reading the propositions in book one of Euclid. I hope to be able to read through about 10 per week while I am about my daily activities. Below I listed the propositions… Read More
2014-02-09 19:46
I recently heard a simple math puzzle on the Math Factor program http://mathfactor.uark.edu/: Suppose that you have two isosceles triangles. The side lengths of one are 5, 5, and 8 unit… Read More
2014-02-01 21:13
Recently we reviewed the Pythagorean theorem with some of my students. We covered the basics of solving for an unknown side and the proof using similar triangles. This year we decided to req… Read More
2014-01-26 02:26
If you have been following my recent blogs, you see that I have been referring to a few dead geometers. I am finished for the time being discussing axioms and definitions. There were of cour… Read More
2014-01-25 00:32
Here below is the axioms presented for comparison for the different sources that I have been citing in the last few posts. You may be interested in comparing them. Similar Axioms are aligned… Read More
2014-01-21 02:54
Below I have made a comparison of some different definitions of some of the first terms in geometry. The first and most basic are point, line, and plane. These are known as undefined terms… Read More
2014-01-12 04:38
Well here it is, my first post on Euclid. I have been teaching high school geometry for years and while Euclid comes up frequently, it generally does so in passing. So there seemed nothing m… Read More
2014-01-06 14:49
Someone once said that the definition of a classic is a book that everyone talks about, but no one reads.Within the next couple weeks I will begin reading the first few books of Euclid's Ele… Read More
2012-09-10 01:17
I thought that you might like a side note math and literature. I made this diagram after reading, "How to Read a Book" by Mortimer Adler over the summer. The observation is basically his, bu… Read More
2012-09-03 07:32
You have probably heard me mention in the past about the beauty in mathematics. This may seem enigmatic to some of you, but this year I started the year by reiterating the primary reasons th… Read More
2012-03-17 14:58
2012-01-15 17:24
I recently finished one of my New Year's resolutions to reread the New Testament. As I concluded my study I read one of the famous passages The Book of the Revelation of Saint John(13:15-18)… Read More
2011-12-22 17:26
Santa-Mas calculations for the jolly.Q. Dear Plebeian how fast does Santa have to go in order to visit each of the world's households on Christmas?A. Santa has to travel about… Read More
2011-04-22 19:22
In the last blog I wrote about how doubling the dimensions of a figure quadruples its area, tripling the dimensions quadruples the area, and quadrupling the dimensions would increase the are… Read More
2011-04-20 04:09
I wanted to talk about radiation levels in Japan and the inverse squares law. However, it is necessary to review a couple basic concepts from geometry first. If two shapes at least have the… Read More
2006-06-07 11:16
I was reading Euclid’s propositions and proofs of the Linear Pair Theorem and converse, and the vertical angles theorem. It finally occurred to me how I should prove the vertical angle… Read More
2006-06-07 11:16
Last summer a coworker and I went to Fresno State and observed debate lessons in geometry. It is a method similar to Socratic seminar. Here is a summary of what it is about. What does a… Read More
2006-06-07 11:16
The new “common core” standards for geometry specifically state that congruence of figures is to be defined by the principle of superposition. In other words, two figures are con… Read More
2006-06-07 11:16
First, I have to apologize. I have been trying to find more convenient ways to add pictures and diagrams to my blogs. The school district where I work is considering abandoning Microsoft Off… Read More
2006-06-07 11:16
Introduction: When I first started blogging as an experiment some of the early posts I made were regarding the philosophical question of defining the field of mathematics. Over time the resp… Read More
2006-06-07 11:16
In my previous post I have already mentioned several axioms things that refer to the flatness of a plane. But there are others that are less obvious. The most famous is known as Euclid's 5th… Read More
2006-06-07 11:16
I have been working mostly by myself for the last couple weeks on a course for the upcoming school year. Thus, I have postponed plans to write. Instead of adopting a pre-made course. I opted… Read More
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