Galileo's Manifesto for Science

Next sectionProlog (On Optimizing the Design of Introductory Mathematics).

      Galileo Galilei

               (1564 - 1642)


Galileo's words still ring true:

"To be placed on the title-page of my collected works:

“Here it will be perceived from innumerable examples what is the use of mathematics for judgment in the natural sciences, and how impossible it is to philosophize correctly without it ... .

“Philosophy is written in that great book which ever lies before our eyes –– I mean the universe –– but we cannot understand it if we do not first learn the language and characters in which it is written. This language is mathematics, and the characters are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”

Authors of the Primer: 

    David Hestenes                                                                                                                         Robert Rowley

Bob chessdavid-hestenes 90K

Professor Emeritus from Arizona State University,
Dr. Hestenes spent his career developing and 
promoting the benefits of Geometric Algebra in
books, scholarly publications, and mentorships.
In that regard, he wrote this primer years ago in
text format.

                              Retired Professor from DeVry University, Bob Rowley
                              (M.S., Physics) is a friend and former student of Dr.
                              Hestenes, and an admirer of the mathematical beauty
                              of GA.  He converted this primer into web pages, and
                              added interactive diagrams and solutions to exercises.

Both men have also taken turns as past chess champions of Arizona.   

Notes for these webpages: 

          These webpages were designed using Sandvox ( which implements HTML5,
                    static diagrams were drawn with Dia ( to get SVG (Scalable Vector Graphics) format, 
                    the interactive diagrams were created with Geogebra (, 
                    and the main math equations use MathJax (www.mathjax.orgto render LaTeX for webpage display. 

          These webpages have been tested using the Safari, Firefox, Chrome, and Internet Explorer (IE) browsers on Mac and Windows
                    computers (XP SP3, Vista, and Windows 7). The results: 

                              IE8 can't run HTML5, but even IE9 failed to display the Geogebra interactive diagrams.
                              Google Chrome 27 worked on all systems but was consistently slowest.
                              Firefox 20 worked and was faster than Chrome.
Safari 5 (and Safari 5 for Windows) worked most reliably and was fastest on these systems.

          Click here if you'd like to download the zipped file of Geogebra interactive diagrams used in this GA Primer.
                    If you're 
connected to the internet, the diagrams are interactive within these webpages,
                    but if you'd like to further explore, see Geogebra's algebra window, or make alterations to the diagrams,
                    download these and the Geogebra software from the website linked above.

          Click here if you'd like to download a PDF version of these webpages for offline viewing.
                    Another useful feature of the PDF version is that it can also be viewed on tablets and smartphones.

Next section: Prolog (On Optimizing the Design of Introductory Mathematics).

© David Hestenes 2005, 2014