The smallest prime number

Any competent mathematician nowadays will agree that two is the smallest prime number, but this was not always the case. There were instances when one (or even three) was considered the smallest prime number. Two recently published papers survey the history of how prime numbers are defined:  “What is the Smallest Prime?” by Chris K. Caldwell and Yeng Xiong (Journal of Integer Sequences, vol. 15 (2012), Article 12.9.7) and “The History of the Primality of One: A Selection of Sources” by Chris K. Caldwell, Angela Reddick, Yeng Xiong, and Wilfrid Keller (Journal of Integer Sequences, vol. 15 (2012), Article 12.9.8).  I think these two papers will be of great use to mathematics educators.

Hot Wheels world records

When I first saw this video of the Hot Wheels Test Facility, I was quite excited and hoped that some of it was real. Although some parts of the HWTF videos are computer-generated, the following three are real:




Team Hot Wheels has broken three world records: the Corkscrew World Record Jump (92-foot long ramp to ramp spiral 360 in a four-wheeled vehicle), the Double Loop Dare World Record (two vehicles racing through a 66-foot tall double vertical loop), and the Fearless at the 500 World Record Jump (332-foot long ramp to ramp jump in a four-wheeled vehicle starting at the top of a 90-foot ramp). (I got the screen captures from the videos at the Team Hot Wheels website.)

Don’t Hug Me I’m Scared

donthugIn a previous blog post I linked to a short film by the This Is It collective.  They made another one called “Don’t Hug Me I’m Scared.”  (The picture above is from a screen capture I made from a version posted at YouTube.) It was entered at the 2012 Sundance Film Festival (where it has the description “A short film about teaching creativity—by This Is It Collective.”) (The film is a little scary and not for kids.)

Plants vs. Zombies: Cobless Again


Here’s a nice Plants vs. Zombies setup I’ve made that doesn’t have any Cob Cannons. It took me around 14 flags to set up, and as you can see below, it’s still going strong at 32 flags. The main problems are the Jack-in-the-Box Zombies which take out the two rightmost plants in the pool, weakening the second and fifth rows.


“Filipinas 2 C. de Peso”

spanishMy friend Patrick and I used to collect stamps when we were young. He gave me the stamp shown on the left.  Based on what I’ve seen on the website The Philippine Philatelist, it seems to be a Philippine stamp issued during the reign of Alfonso XIII, King of Spain from 1886 to 1931, when the Philippines was a Spanish colony.  I’m trying to identify it.  Four candidates are shown below (from left to right):  a 2 centavos violet issued February 1, 1892, a 2 centavos dark brown issued January 1, 1894, a 2 centavos ultramarine issued January 1, 1896, and a 2 centavos gray brown issued January 1, 1896. (Click on the pictures to see where I got them.)  I think my stamp is a violet one.


Here’s a sample post from a nice WordPress site with free printable Filipino worksheets.


I finally completed my first set of Filipino worksheets for preschool kids!

This is a 7-page set of handwriting worksheets designed to help a child practice writing the 28 letters of the Filipino alphabet (Alpabetong Filipino).  Each page has four letters.  Each letter is accompanied by a word (and its illustration) that begins with or uses the letter. Thumbnails of the worksheets are shown below.

All illustrations in this set of worksheets are by samutsamot_mom. Feel free to download, print, and photocopy these worksheets for your students or children. Please do not copy or distribute these worksheets for profit. If you click the link below, you will download all seven pages of the pdf file.

Alpabetong Filipino_1

A to D E to HI to LM to NgO to R S to VW to Z

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Goodbye, multiply

(Originally posted at on October 15, 2012 8:49 PM)

I now have a new blog at  (I could not register the domain name because it is reserved.)  I’m currently in the process of copying my multiply blog entries to WordPress, and I expect to finish the move in the next few days.  This is my last blog entry in multiply.

Thomas Harriot’s Artis Analyticae Praxis: A first look

(Originally posted at on
September 14, 2012 9:56 AM)

sg07 harriot7

A few months ago, I bought a copy of Seltman and Goulding’s Thomas Harriot’s Artis Analyticae Praxis: An English Translation with Commentary (Springer, 2007) at a BOOKSALE outlet.

Thomas Harriot‘s Artis Analyticae Praxis (The Practice of the Analytic Art) was published in 1631 in Latin, ten years after his death.  (I got the picture on the right from here.)

From Seltman and Goulding’s Introduction (p. 1):

In the algebraic work of Thomas Harriot, it was above all his notation that was revolutionary.  His algebra was the first to be totally expressed in a purely symbolic notation […].

Yet, Harriot is known in general histories of mathematics principally for certain technical innovations in algebra—for the invention of the inequality signs, for equating the terms of a polynomial equation to zero, and for generating such equations from the product of binomial factors, thereby displaying their structure.

I have not read much of Seltman and Goulding’s book, but as a mathematics educator I find Harriot’s work very interesting.  It seems that he was the originator of the decimal digit-by-digit method of obtaining square roots that I was taught in elementary school.

The Artis Analyticae Praxis has two parts; the first has six sections serving as preparatory material for the second part, which is about “the numerical solution of [polynomial] equations by the method of successive approximation” (p. 13).  Harriot builds upon previous work by François Viète, making it “more convenient and practical” (p. 4).

It is quite unfortunate that Seltman and Goulding’s book has numerous typographical errors, many to do with incorrect hyphenation (for example, “The-re” on p. 2, “ha-ve” on p. 12, “tho-se” on p. 20, and so on) and alignment of columns in tables (such as on p. 132).

When I have the time I would like to study this book in more detail.  I feel that it has some exciting insights that can easily be explained by college teachers to their undergraduate students.