# Bibliography Related To Motivational Posters

## Annotated Bibliography

Related to Geometry

### Last Updated: August 2004

### Any additions or corrections are welcomed. Send to dwh2@cornell.edu

#### Most of these books (and articles) are in my personal library – they are grouped into subject matter sections. The remainder I have read or consulted in connection with the writing of my books. The annotations in quotes (" ") are taken from the listed book, usually from the Preface.When available I have included links to online versions of the book. In addition, the The University of Michigan historic books collection contains many geometry books that may be of interest – some of these are listed at the end.

Sections:

AD. Art and Design

AG. Analytic Geometry

AN. Analysis

AT. Ancient Texts

CA. Calculus

CE. Cartography, the Earth

CG. Computers and Geometry

CT. College Teaching

DC. Dissections and Constructions

DG. Differential Geometry

DS. Dimensions and Scale

EG. Expositions - Geometry

EM. Expositions - Mathematics

FO. Foundations of Geometry

FR. Fractals

GC. Geometry in Different Cultures

GS. Geometry and Science

HI. History of Mathematics

HM. History of a Mathematician

HY. Hyberbolic Geometry

IN. Inversions

LA. Linear Algebra and Geometry

LS. Learning/Students

ME. Mechanisms

MI. Minimal Surfaces

MP. Models and Polyhedra

MS. Mathematics and Social Issues

NA. Nature

PA. Projective and Affine Mathematics

PH. Philosophy of Mathematics

RN. Real Numbers

SA. Sacred Geometry

SG. Symmetry and Groups

SP. Spherical Geometry

TG. Teaching Geometry

TM. Teaching Mathematics

TP. Topology

TX. Geometry Texts

UN. The Physical Universe

University of Michigan historic books collection

** **

**AD. Art and Design**

Albarn, Keith, Smith, Jenn Mial, Steele, Stanford, and Walker, Dinah. *The Language of Pattern*. New York: Harper & Row, 1974.

Inspired by Islamic decorative pattern, the authors of this book, who are all designers, explore pattern step by step, beginning with simple numerical and geometrical relationships and progressing through the dimensions

Alexander, Christopher, Ishikawa, Sara, and Silverstein, Murray. *A Pattern Language: Towns, Bulidings, Construction*. New York: Oxford University Press, 1977.

A pattern language for building

Auvil, Kenneth W. *Perspective Drawing*. Mountain View, CA: Mayfield Publishing, 1997.

Baglivo, Jenny A. and Graver, ack E. *Incidence and Symmetry in Design and Architecture*. New York: Cambridge University Press, 1983.

"The purpose of this text is to develop mathematical topics relevant to the study of the incidence and symmetry structures of geometrical objects. A secondary purpose is to expand the reader's geometric intuition. The two fundamental mathematical topics employed in this endeavor are graph theory and the theory of transformation groups."

Bain, George. *Celtic Arts: The Methods of Construction*. London: Constable, 1977.

A description of the construction of Celtic patterns and designs.

Blackwell, William. *Geometry in Architecture*. New York: John Wiley & Sons, 1984.

William Blackwell offers a basic review of the fascinating relationships that exist in linear design. At the same time, he uncovers new geometric principles and new applications of geometry that may have a major influence on the state of architecture today.

Coxeter, H.S.M., Emmer, M., Penrose, R., and Teuber, M.L:.*M.C. Escher: Artand Science*,New York: Elseview Science Publishing Co., Inc., 1986.

Doczi, György. *The Power of Limits*. Boulder, CO: Shambhala, 1981.

Edgerton, Samuel Y., Jr. *The Heritage of Giotto's Geometry Art and Science on the eve of the Scientific Revolution*. Ithaca: Cornell University Press, 1993.

A historical account of the development of perspective in the art of the Italian Renaisance.

Edmondson, Amy C. *A Fuller Explanation:The Synergetic Geometry of R. Buckminster Fuller*. Boston: Birkhauser, 1987.

An account of the geometry and design ideas of Fuller.

Elam, Kimberly. *Geometry of Design: Studies in Proposition and Composition*. New York: Princeton Architectural Press, 2001.

"This book seeks to explain visually the principles of geometric composition and offers a wide selection of professional posters, products, and buildings that are visually analyzed by these principles."

Emmer, Michele:.*The Visual Mind: Art and Mathematics*,Cambridge: MIT Press, 1993.

Ernst, Bruno. *The Magic Mirror of M.C. Escher*. New York: Random House, 1976.

Throughout the book Bruno Ernst describes in detail the conception and execution of Escher's popular prints, showing with the aid of sketches and diagrams how the artist arrived at such astonishing creations as "The Balcony" and "Print Gallery." Careful attention is also paid to the graphic techniques Escher employed so successfully."

Escher, M.C. *The Graphic Work of M.C*. New York: Hawthorn Books,Inc.,Publishers, 1960.

It is a fact, however, that most people find it easier to arrive at an understanding of an image by the round-about method of letter symbols than by the direct route. So it is with a view to meeting this need that I myself have written the text.

Field, Judith Veronica. *The Invention of Infinity: Mathematics and Art in Renaissance*. Oxford: Oxford University Press, 1997.

Book will look at the relations between of Renaissance art and mathematics in the period from about 1300 to about 1650.

Fomenko, Anatolii. *Mathematical Impressions*. Providence,Rhode Island: American Mathematical Society, 1991.

This book contains more than 80 reproductions of works by Fomenko. In the accompanying captions, Fomenko explains the mathematical motivation behind the illustrations as well as the emotional, historical, or mythical subtexts they evoke.

Ghyka, Matila. *The Geometry of Art and Life*. New York: Dover Publications, 1977.

Gombrich, Ernst. *The Sense of Order: A Study in the Psychology of Decorative Art*. Ithaca, NY: Cornell University Press, 1978.

Henderson, Linda. *The Fourth Dimention and Non-Euclidean Geometry in Modern Art*. Princeton,NJ: Princeton University Press, 1983.

Hersey, George L. *Architectgure and Geometry in the Age of the Baroque*. Chicago: The University of Chicago Press, 2000.

Holt, Michael. *Mathematics in Art*. London: Studio Vista, 1971.

This book is not an account of either specialism of the title; that I leave to the acknowledged experts. Rather it is an attempt to focus on aspects common, it seems to me, to both mathematics and the visual arts. These aspects form then an anthology of creative highlights that have caught my eye.

Ivins, William M., Jr. *Art & Geometry: A Study In Space Intuitions*. New York: Dover Publications, 1946.

Jacobs, Michael and Fernández, Francisco. *Alhambra*. New York: Rizzoli, 2000.

Kappraf, Jay. *Connections: The Geometric Bridge between Art and Science*. New York: McGraw-Hill, 1991.

There is a hidden harmony in the works of man and nature. From the great pyramid of Cheops to patterns of plant growth, natural and artificial designs are all governed by precise geometric laws. Design Science is the study of these hidden laws; it is the search for the connections underlying all that is beautiful and functional.

King, Ross. *Bruelleschi's Dome: How a Renaissance Genius Reinvented Architecture*. New York: Penquin Books, 2000.

Linn, Charles. *The Golden Mean: Mathematics and the Fine Arts*. Garden City, NY: Doubleday, 1974.

Lord, E.A. and Wilson, C.B. *The Mathematical Description of Shape and Form*. New york: Halsted Press, 1986.

"Thus, in this survey, we are not presenting a compendium of unrelated mathematical techniques. Instead, we have attempted to present a unified view of the mathematics of form description, emphasising underlying mathematical principles."

Miyazaki, Kojiv. *An Adventure in Multidimensional Space*. New York: John Wiley and Sons, Inc., 1983.

The art and geometry of polygons, polyhedra, and polytopes.

Schattschneider, Doris. *Visions of Symmetry : Notebooks, Periodic Drawings, and Related Work of M.C. Escher*. WH Freeman & Co, 1992.

Schattschneider, Doris, and Emmer, Michele:.*M. C. Escher's Legacy:A Centennial Celebration*,New York: Springer-Verlag, 2003.

The book features 40 articles, most by presenters at the Escher Centennial Congress in Rome and Ravello in 1998 and others. There is a rich array of illustrations, both of Escher's work and of original work by the authors.The CD Rom supplements the book with presentations of art (in color), as well as some videos, animations, and demo software.

Schneider, Michael S. *A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science*. New York: HarperPerennial, 1994.

Strosberg, Eliane. *Art and Science*. New York: Abbeville Press, 2001.

Taylor, Anne. *Math in Art*. Hayword, CA: Activity Resources Co., Inc., 1974.

This book has been developed to show children the unique relationship between art and math and to help them discover concepts in each areas, as they relate to each other.

Watson, Ernest W. *Creative Perspective for Artists and Illustrators*. Mineola, NY: Dover Publications, 1992.

Williams, Robert. *The Geometrical Foundation of Natural Structure: A Source Book of Design*. 1979: Dover, 1979.

de Vries, Jan Vredeman. *Perspective*. New York: Dover, 1968.

Reproductions of engravings from the 1604/1605 edition. Warning: Some of the engravings have geometrically incorrect perspective.

AG. Analytic Geometry

Hahn, Liang -shin. *Complex Numbers & Geometry*. Washington DC: Mathematical Association of America, 1994.

The purpose of the book is to demonstrate that these two subjects can be blended together beautifully, resulting in easy proofs and natural generalizations of many theorems in plane geometry.

Kuipers, Jack B. *Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality*. Princeton: Princeton University Press, 1999.

"This book is intended for all those mathematicians, engineers, and physicists who have to know, or who want to know, more about the modern theory of quaternions. Primarily, as the title page suggests, it is an exposition of the quaternion and its primary application as a rotation operator."Included are applications of spherical geometry.

Postnikov, M. *Lectures in Geometry Semester I Analytic Geometry*. Moscow: MIR publishers, 1982.

The subject matter is presented on the basis of vector axiomatics of geometry with special emphasis on logical sequence in introduction of the basic geometrical concepts.

Schwerdtfeger, Hans. *Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry*. New York: Dover Publications, Inc., 1979.

This book uses complex numbers to analyze inversions in cricles and then their relationship to hyperbolic geometry.

Smogorzhevsky, A.S. *The Method of Coordinates*. Moscow: Mir Publishers, 1984.

From a collection of short books (phamphlets) for high school students written by Soviet mathematicians and translated into English.

AN. Analysis

Bishop, Errett and Douglas,Bridges. *Constructive Analysis*. New York: Springer-Verlag, 1985.

The main book on constructive analysis.

Bressoud, David. *A Radical Approach to Real Analysis*. Washington, DC: Mathematical Association of America, 1994.

Goldblatt, Robert. *Lectures on the Hyperreals*. New York: Springer, 1998.

Hairer, E. and Wanner, G. *Analysis by Its History*. New York: Springer, 1996.

Rudin,Walter. *Principles of Mathematical Analysis*. New York: McGraw Hill, 1964.

For many years a standard text in analysis.

Strichartz, Robert S. *The Way of Analysis*. Boston: Jones and Bartlett Publishers, 1995.

The presentation of the material in this book is often informal. A lot of space is given to motivation and a discussion of proof strategies." This is only recent analysis book that I know of that is direct and honest about Archimedean Axiom.

AT. Ancient Texts

AL-Khawarizmi, Muhammad Ibn Musa. *Al-Jabr wa-l-Muqabala*. Baghdad: House of Wisdom, 825.

Traslated in English in Karpinski, L.C., ed., Robert of Chester's Latin Translation of Al'Khowarizmi's Algebra, New York: Macmillan, 1915.

Perga, Apollonius of. *On Cutting Off a Ratio*. Fairfield: The Golden Hind Press, 1987.

An Attempt to Recover the Original Argumentation through a Critical Translation of the Two Extant Medieval Arabic Manuscript.

Perga, Apollonius of. *Treatise on Conic Sections*. New York: Dover, 1961.

This is the standard work on conic sections from the Greek world.

Baudhayana. *Sulbasutram*. Bombay: Ram Swarup Sharma, 1968.

This is translated from the Sanskrit manual for the construction of alters. The beginning of the book contains a discussion the geometry needed for the construction of the altars this beginning section is apparently the oldest surviving geometry textbook.

Berggren, J. Lennart and Jones, Alexander. *Ptolemy's /it Geography : an annotated translation of the theoretical chapters*. Princeton, NJ: Princeton University Press, 2000.

Berggren, J.L. and Thomas, R.S.D. *Euclid's Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy*. New York: Garland Publishing, 1996.

Contains the only accessible English translation of Euclid's *Phaenomena*. This work is, alas, out of print, but a brief, and more easily obtained account of its comments can be found in: Berggren, J.L., and Thomas, R.S.D.,"Mathematical Astronomy in the Fourth Century B.C. as found in Euclid's Phaenomena", *Physis*, Vol XXIX (1992), 7-33.

Bonasoni, Paolo. *Algebra Geometrica*. Annapolis: The Golden Hind Press, 1985.

being the only known work of this nearly forgotten Renaissance mathematician (excepting a still unpublished treatise on the division of circles).

Cardano, Girolamo. *The Great Art or the Rules of Algebra*. Cambridge: MIT Press, 1968.

This is the book that first describes algebraic algorithms for solving most cubic equations.

Coxeter, H.S.M. and Greitzer, S.L. *Geometry Revisited*. New York: The L.W. Singer Company, 1967.

"Using whatever means will best suit our purposes, let us revisit Euclid. Let us discover for ourselves a few of the newer results. Perhaps we may be able to recapture some of the wonder and awe that our first contact with geometry aroused."

Descartes, Rene. *The Geometry of Rene Descartes*. New York: Dover Publications,Inc., 1954.

This the book in which Descartes develops the use of what we now call Cartesian coordinates for the study of curves.

Euclid: Phaenomena. *Euclidis opera omnia*. Menge H, (eds). anonymous Lipsiae, B.G. Teubneri, 1883,

Euclid:*Optics*, . *Journal of the Optical Society of America* 35, no. 5 (1945), 357-372.

This is a translation of Euclid's work that contains the elements of what we now call perjective geometry.

Euclid. *Elements*. New York: Dover, 1956.

This is edition of Eulid's Elements to which one is usually referred. Heath has added a large collection of very useful historical and philosophical notes.

Euclid. *Elements*. London: Dent & Sons, 1933.

Todhunter's translation of Euclid.

Euclid. *Elements*. Green Lion Press, 2002.

Thomas L. Heath translation, edited by Dana Densmore, all in one volume without Heath extensive notes

Galilei, Galileo: Trattato della Sphaera (1586-87). *Galilei Opere*. Favaro A, (eds). anonymous Florence, G. Barbera, 1953,

Guthrie, Kenneth. *The Pythagorean Sourcebook and Library*. Grand Rapids: Phanes Press, 1987.

An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy.

Heath, T.L. *Euclid: The Thirteen Books of the Elements*. New York: Dover, 1956.

This is edition of Eulid's Elements to which one is usually referred. Heath has added a large collection of very useful historical and philosophical notes. His notes are more extensive than Euclid's text.

Karpinski, L.C.:.*Robert of Chester's Latin Translation of Al'Khowarizmi's Algebra*,New York: Macmillan, 1915.

Khayyam, Omar:* a paper(no title)*, . *Scripta Mathematica* 26 (1963), 323-337.

In this paper Khayyam discusses algebra in relation to geometry.

In this paper Khayyam discusses algebra in relation to geometry.

Khayyam, Omar. *Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis*. Alexandria, Egypt: Al Maaref, 1958.

Khayyam, Omar. *Algebra*. New York: Columbia Teachers College, 1931.

In this book Khayyam gives geometric techniques for solving cubic equations.

Plato. *The Collected Dialogues*. Princeton,NJ: Bollinger, 1961.

Plato discusses mathematical ideas in many of his dialogues.

Plotinus. *The Enneads*. Burdette, NY: Larson Publications, 1992.

Proclus. *Proclus: A Commentary on the First Book of Euclid's Elements*. Princeton: Princeton University Press, 1970.

These commentaries by Proclus (Greek, 410-485) are a source of much of our information about the thinking of mathematicians toward the end of the Greek era.

Saccheri, Girolamo. *Euclides Vindicatus*. New York: Chelsea pub. Co., 1986.

In this book Girolamo Sacchri set forth in 1733, for the first time ever, what amounts to the axiom systems of non-Euclidean geometry." It is not mentioned in this volume that Saccheri borrowed many ideas from Khayyam's Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis.

Smyrna, Theon of. *Mathematics Useful for Understanding Plato*. San Diego: Wizards Bookshelf, 1978.

This work appears to have been a text book intended for students who were beginning a study of the works of Plato. In its original form there were five sections: 1) Arithmetic 2) Plane Geometry 3) Stereometry (solid geometry) 4) Music 5) Astronomy. Sections 2 and 3 on Geometry have been lost while the others remain in their entirety and are presented here." The section on Astronomy contains discussions of the shape of space.

Thomas, Ivor:.*Selections Illustrating the History of Greek Mathematics*,Cambridge, MA: Harvard University Press, 1951.

A collection of primary sources.

CA. Calculus

Amdahl, Kenn and Loats, Jim. *Calculus For Cats*. Broomfield, CO: Clearwater Publishing, 2001.

Berlinski, David. *a tour of the calculus*. New York: Pantheon Books, 1995.

Cohen, David W.: Henle, James M. *Conversational Calculus*. Reading, MA: Addison-Wesley, 1997.

Mayo, M.J. (2009b). *Bringing game-based learning to scale: The business challenges of**serious gaming.* Paper presented at the National Research Council Workshop on Gaming and Simulations, October 6-7, Washington, DC. Available: http://www7.nationalacademies.org/bose/Mayo_Gaming_CommissionedPaper.pdf [accessed April 5, 2010].

McQuiggan, S.W., Robison, J.L., and Lester, J.C. (2008). *Affective transitions in**narrative-centered learning environments.* Paper presented at the Proceedings of the Ninth International Conference on Intelligent Tutoring Systems, Montreal, Canada.

Meir, E., Perry, J., Stal, D., Maruca, S., and Klopfer, E. (2005). How effective are simulated molecular1 level experiments for teaching diffusion and osmosis? *Cell**Biology Education*, *4*, 235-248.

Messick, S. (1994). The interplay of evidence and consequences in the validation of performance assessments. *Educational Researcher, 32*, 13-23.

Metcalf, S.J., Clarke, J. and Dede, C. (2009). *Virtual worlds for education: River city**and EcoMUVE*. Paper presented at the Media in Transition International Conference, MIT, April 24-26, Cambridge, MA.

Meyer, A., and Rose, D.H. (2005). The future is in the margins: The role of technology and disability in educational reform. In D.H. Rose, A. Meyer, and C. Hitchcock (Eds.), *The universally designed classroom: Accessible curriculum and digital**technologies* (pp. 13-35). Cambridge, MA: Harvard Education Press.

Mitchell, T.M. (1997). *Machine Learning.* New York: McGraw-Hill.

Miller, J.D. (1998). The measurement of civic scientific literacy. *Public Understanding**of Science, 7*(3), 203-223.

Miller, J.D. (2001). The acquisition and retention of scientific information by American adults. In J.H. Falk (Ed.), *Free-choice science education: How we learn science**outside of school* (pp. 93-114). New York: Teachers College Press.

Miller, J.D. (2002). Civic scientific literacy: A necessity for the 21st century. *Public**Interest Report: Journal of the Federation of American Scientists, 55*(1), 3-6.

Miller, J.D., Pardo, R., and Niwa, F. (1997). *Public perceptions of science and technology: A comparative study of the European Union, the United States, Japan, and**Canada.* Madrid: BBV Foundation Press.

Mislevy, R.J., and Gitomer, D.H. (1996). The role of probability-based inference in an intelligent tutoring system. *User-Modeling and User-Adapted Interaction*, *5,* 253-282.

Mislevy, R.J., Chudowsky, N., Draney, K., Fried, R., Gaffney, T., Haertel, G., Hafter, A., Hamel, L., Kennedy, C., Long, K., Morrison, A.L., Murphy, R., Pena, P., Quellmalz, E., Rosenquist, A., Songer, N., Schank, P., Wenk, A., and Wilson, M. (2003). *Design patterns for assessing science inquiry* (PADI Technical Report 1)*.* Menlo Park, CA: SRI International, Center for Technology in Learning.

Moreno, R., and Mayer, R.E. (2000). Engaging students in active learning: The case for personalized multimedia messages. *Journal of Educational Psychology*, *92*, 724-733.

Moreno, R., and Mayer, R.E. (2004). Personalized messages that promote science learning in virtual environments. *Journal of Educational Psychology*, *96*, 165-173*.*

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