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History of Mathematics Archive

Author(s): 
Don Crossfield, reviewer

This site, http://archives.math.utk.edu/topics/history.html, is pretty overwhelming, with all of its very neat stuff.   Don’t start exploring unless you have at least a couple of free hours ahead of you.  Here are some comments about its attractive reference links:

 

Abacus in Various Number Systems

The best part is the Internet reference at the bottom.  It’s awesome.  I wandered there happily for a half hour.  It was very fun exploring.  There is a precious article about Dr. Feynman and an abacist in an arithmetic duel, with some good philosophical observations.

Abacus: The Art of counting with Beads

The highlight for me was in the Roman Hand Abacus article.  The author talked about a mixed base abacus, one whose columns held differing numbers of beads in differing arrangements.  It’s intriguing to picture one of those as perhaps a way to measure time, or convert from teaspoons to gallons.

Biographies of Women Mathematicians

This site is jazzed up with a radio interview of Danica McKellar, the actress who played Winnie on Wonder Years, and other modern multiple talented mathematicians.  I spent 50 minutes here and enjoyed every one.

Earliest Known Uses of Some Words of Mathematics

Did you know that the word "degree" (as in angle measure) was used by Chaucer in Canterbury Tales in 1386?  Check out the site to find out how.  At the bottom of that site is a wonderful site called, Images of Mathematicians on Postage Stamps. Teachers will have many appropriate pictures to enhance their lessons from this site.  Samples include Fermat with his recently proven Last Theorem, and multiple versions of Euler-result stamps, one with V+F-E=2, and another with eix = cos x + i sin x.   Don’t start exploring here unless you have time.

Another great website at the bottom here is Ambiguously Defined Terms at the High School Level.  It discusses the confusion that occurs with the words trapezoid, critical point, amplitude of a curve, simplified form, standard form, and many other phrases whose usage differs in various parts of the world.

Ethnomathematics on the Web

Before I knew it, I was sucked down into African American Cornrow Curves using Transformational Geometry, and was learning how to braid hair using patterns which illustrate translation, reflection, rotation and dilation.   If my hair were sufficiently long and pliable, and my wife sufficiently patient, I would be sporting a new look in the classroom Monday morning.

The geometry of Oriental carpets, of Islamic art, and Hawaiian quilts, as well as an intriguing paper on naming relatives in Hawaiian family trees, make this a captivating site.

Front for the XXX Mathematics Archive - History and Overview

Oh my goodness.  There is such a plethora of playground for the Philomath here.  Just start exploring.  Looking at Euler’s writings alone would cause you to want to retire, both to find the time to read them and also because we mortals could never hope to replicate that level of industry.

The Geometry of War

There are over a hundred pictures of instruments and techniques created during the Renaissance for such military concerns as navigation, surveying, cartography, artillery accuracy, fortification and troop formation.  Good information, well organized.

Greek Mathematics and Its Modern Heirs

The best site I’ve seen for pictures of ancient Greek manuscripts.  Good material to introduce a topic in a classroom setting.

Henry Perigal’s Monument

Don’t be fooled by the opening site.   Go on to the link to Dissections, Plane and Fancy and you’ll see a whole garden of interesting places to play.

History of Mathematics, David Joyce

A portal into a HUGE collection of links.  I think every mathematics website I’ve ever used is somehow accessible from this site.

History of Mathematics, Trinity College , Dublin

The focus is on British mathematics of 1600-1800, of which there is much to be said.  Good links to all things Newton , Hamilton, Riemann, Berkeley, and others from that time period.

Hypatia of  Alexandria

Much more than I ever suspected.   I think this is the comprehensive/exhaustive collection of all the modern world knows about Hypatia.  I was impressed.

Legacy of R.L. Moore Project

Every educator should at some time carefully consider the tenets of Moore ’s educational system.  This site is sufficiently dense so that one can get a good idea of what he believed and a feeling for how it might be a very successful style of teaching.  Worth exploring if you are unfamiliar with R.L. Moore.

MacTutor History of Mathematics

This is my very favorite site for exploring mathematics and its history.  It’s been around for awhile, and yearly improves its ease of use and its depth of material.  My students are invariably astounded at the breadth of material available on mathematicians, on curves, and on special historically famous mathematical events.  Regardless of what math topic we are studying, they can find relevant pages in this site.

Materials for the History of Statistics

I was browsing through this well ordered site, enjoying the collection of fun statistical graphs, names, links, and a section on game theory, when I hit a link to fun statistical quotes.  As you no doubt realize, statistics is a ripe arena for fun quotations.  An analysis of Dungeons and Dragons read: “Here we have a game that combines the charm of a Pentagon briefing with the excitement of double-entry bookkeeping.”  A half hour later, I’d read only 20 pages of the quotes and remembered that I was supposed to be reviewing a website.  I hope you enjoy getting sidetracked as much as I did.  The only drawback to this site was that its link to Convergence didn’t work.

Mathematical Connections

Don’t slide by this one, because of the Humanities emphasis.  There’s a cute article about teaching the Golden Ratio, and several others with some meat, in a fun context.

Mathematical Problems (Hilbert’s Famous 1900 Lecture)

This lecture is one of the most famous in all of mathematics, because here Hilbert gives a list of the most pressing and important problems facing the 20th century.  In hindsight, we can see that they truly were, and are, incredibly significant 100 years later.  A few have been solved, a few dented, but the others are still alive and kicking, despite being poked at by 3 more generations of mathematicians.

A Sideways Look At Hilbert’s 23 Problems of 1900

This is a commentary on the lecture, and gives more flesh to the concepts, more history behind the problems, and more information about progress that has been made.  It’s a very good supplement to the lecture itself, in which Hilbert actually only talked about a few of the 23 problems.

Mathematicians of the African Diaspora (A History of Blacks in Mathematics)

Well done, seemingly thorough, and easy to read.  This site should be available to educators to help dispel the notion that mathematics was a uniquely European/Caucasian undertaking, despite the prevalence of links to mathematicians of that ethnicity.

Mathographies

The biographies themselves aren’t any better than MacTutor, but at the bottom, you’ll find a link called Math on the Web, which actually leads to MacTutor, AND to a great many more useful locations.  One called Top Six PreCalculus Resources was very comprehensive and one that I will give my students this fall.

Mathworld-History and Terminology

This is a Wolfram Technology site.  Wolfram is responsible for Mathematica, and the site is both deep and wide.  I wandered in and quickly found a page that claimed that the Pythagorean triple [3 4 5], written purposely as a 1x3 matrix, could be turned into any other primitive triple, by multiplying by a finite number of matrices U, D, and L, each given in the site.  That’s one MORE reason this review is taking so long.  Isn’t mathematics wonderful?

Mesopotamian Mathematics

Often considered to be the cradle of mathematics civilization, Mesopotamia has been given short shrift in most mathematics courses.  This site remedies that nicely.  It shows the famous square root of 2 tablet, the one that gives a remarkably good approximation for the ratio between the diagonal and side of a square. It also gives an expanded account on the role reciprocals played in Babylonian mathematics.

Sangaku, Japanese Temple Geometry Problems

The topic is a fascinating one.   The website gives examples of such temple problems, but not nearly enough links to capture one’s interest.  Here are some web addresses that should have been linked to this site.:

www.sangaku.info/   

www.cut-the-knot.org/Curriculum/Geometry/TwoCirclesInThirdSangaku.shtml

www.loyola.edu/maru/sangaku.html

www.paginar.net/matias/articles/sangaku/sangaku.html

www.georgehart.com/sangaku/

Teaching with Original Historical Sources in Mathematics

Professors Pengelley and Laubenbacher have developed over the years a course that uses the original sources of great mathematical works as its teaching cornerstone.  They have had great success with this approach, and this website chronicles their curriculum.  There is a very large collection of material, with numerous links, to permit the viewer to get a good feeling for how this approach manifests itself in the classroom.  This is another site that takes much time to peruse.

Thoughts on Ancient Egyptian Mathematics

This is a solitary site, with no links, but the author makes a reasoned case that the sophistication of Egyptian mathematics was higher than the commonly quoted Rhind Papyrus and Moscow Papyrus have led scholar to believe- well worth reading!

 

Don Crossfield, Roseburg H.S. , Roseburg, OR

 

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