Math

This page has useful math links. You should also check the Lill’s method page and the papers page.

Important math websites

https://oeis.org/ – The On-Line Encyclopedia of Integer Sequences (OEIS). The importance of this database can be summarized by this opinion piece by Doron Zeilberger.

https://www.wolframalpha.com/ – a very useful answer engine.

Interesting math websites

https://sites.math.rutgers.edu/~zeilberg/OPINIONS.html – Opinion pieces by Dr. Doron Zeilberger. On the Wikipedia page they call his opinions “provocative”. Good to see people that question some of the main stream ideas .

http://intellectualmathematics.com/ – The website of Dr. Viktor Blasjo. He has interesting opinions on the history of math and math education. For his criticism of Galileo, he deserves the title of Galileomastix (Galileo whipper, see Zoilus, Homer and Homeromastix for comparison).

https://www.quadrivium.info/ – a website dedicated to math education. David Dennis’s math history papers are very interesting, especially for people like me that believe that there should be a greater equilibrium between algebra and geometry.

https://www.c82.net/euclid/ – this is an interactive reproduction of Oliver Byrne’s Euclid. In 1847 Byrne published an edition of Euclid’s Elements that contained the first 6 books (out of 13).  His version is famous for its innovative use of colors and graphics to explain Euclid’s propositions. Most of the words are replaced by colorful diagrams, keeping the number of words to a minimum. The man behind the interactive website is Nicholas Rougeux.

http://pentagonia.ro/ – this is a Romanian blog that belongs to Constantin Titus Grigorovici. The main topic of the blog is math education in Romania (especially K-12 education). I learned a lot about the history of math education from this blog.

Visual Mathematics

SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning – This is a good paper to start reading if you are interested in visual mathematics and education. It cites other papers that show the relationship between mathematical thinking and visual thinking or processing. At the end it has a few helpful tips for teachers who want to apply visual techniques in their classroom.

1543 AND ALL THAT – This is a good paper to start reading if you are interested in visual mathematics and education. It cites other papers that show the relationship between mathematical thinking and visual thinking or processing. At the end it has a few helpful tips for teachers who want to apply visual techniques in their classroom.

Graphical and Mechanical Methods for Solving Polynomial Equations

Machines for Solving Algebraic Equations – This paper is 17 pages long if we include the references. People interested in the history of mechanical and electro-mechanical equation solvers should read this paper. It cites about 58 sources that can be very useful for additional research.

A mechanism for solving: equations of the nth degree – This is a paper by Dr. R.F. Muirhead. The mechanical devices discussed in this paper are very simple devices made of bars. He discusses how to make a device to solve polynomial equations and devices that can solve systems of equations (even systems of non-linear equations).

Machine for solving numerical equations – This is a link to an article that describes a machine proposed by George B. Grant. The device is a scale with multiple horizontal beams, and can be used to calculate the real roots of a polynomial equation. The coefficients are represented by the mass of the weights, with the negative or positive sign being determined by the position of the weights to the left side or the right side of the scale.

Two Hydraulic Methods to Extract the nth Root of Any Number – The link contains 2 articles by Dr. Arnold Emch. The second article extends the first method discussed in the first article in order to make the method applicable to a general polynomial of degree n.