Geometry and Topology
http://www.maa.org/taxonomy/term/41782/0
enLearning Geometry in Georgian England
http://www.maa.org/publications/periodicals/convergence/learning-geometry-in-georgian-england
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The copybooks of two young men reveal very different purposes in learning geometry.</p>
</div></div></div>Why Are the Gergonne and Soddy Lines Perpendicular? A Synthetic Approach
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/why-are-the-gergonne-and-soddy-lines-perpendicular-a-synthetic-approach
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author gives a synthetic geometric proof answering the question in the title of the paper.</em></p>
</div></div></div>Proof Without Words: Tangent of the Sum
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/proof-without-words-tangent-of-the-sum
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The tangent of the sum formula is proved by using an inscribed quadrilateral whose longest side is the diameter of the circle, and the diagonals are perpendicular to the pair of oposite sides, respectively.</em></p>
</div></div></div>The Utility of Catenaries to Electric Utilities
http://www.maa.org/programs/faculty-and-departments/course-communities/the-utility-of-catenaries-to-electric-utilities
Maya Geometry in the Classroom
http://www.maa.org/publications/periodicals/convergence/maya-geometry-in-the-classroom
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>How Classic Maya people probably used knotted ropes to form desired geometric shapes in art and architecture</p>
</div></div></div>A Political Redistricting Tool for the Rest of Us
http://www.maa.org/publications/periodicals/a-political-redistricting-tool-for-the-rest-of-us
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In the United States, congressional districts are redrawn every ten years based on changes in population revealed by the census. Individual states are responsible for redrawing their congressional districts. Often sophisticated (and expensive) software packages are used to guide redistricting committees when drawing the new boundaries. Much of the cost is due to the fact that redistricting is a fantastically complicated problem. We do not propose to give a definitive way of building political districts.</p></div></div></div>The Japanese Theorem for Nonconvex Polygons
http://www.maa.org/publications/periodicals/loci/the-japanese-theorem-for-nonconvex-polygons
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Abstract</strong>. The so-called "Japanese theorem" dates back over 200 years; in its original form it states that given a quadrilateral inscribed in a circle, the sum of the inradii of the two triangles formed by the addition of a diagonal does not depend on the choice of diagonal. Later it was shown that this invariance holds for any cyclic polygon that is triangulated by diagonals. In this article we examine this theorem closely, discuss some of its consequences, and generalize it further.</p></div></div></div>Cubes, Conic Sections, and Crockett Johnson
http://www.maa.org/publications/periodicals/convergence/cubes-conic-sections-and-crockett-johnson
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Children’s book author and painter's interest in doubling the cube</p>
</div></div></div>A Pair of Articles on the Parallelogram Theorem of Pierre Varignon
http://www.maa.org/publications/periodicals/convergence/a-pair-of-articles-on-the-parallelogram-theorem-of-pierre-varignon
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Varignon and his theorem in your classroom</p>
</div></div></div>Unreasonable Effectiveness of Knot Theory
http://www.maa.org/publications/periodicals/convergence/unreasonable-effectiveness-of-knot-theory
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Knot theory's surprising applications in physics.</p>
</div></div></div>Euclid21: Euclid's Elements for the 21st Century
http://www.maa.org/publications/periodicals/convergence/euclid21-euclids-elements-for-the-21st-century
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The classic text presented dynamically and interactively via its logical dependencies</p>
</div></div></div>Led Astray by a Right Triangle: Misconception, Epiphany, and Redemption
http://www.maa.org/publications/periodicals/convergence/led-astray-by-a-right-triangle-misconception-epiphany-and-redemption
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>An error in the study of ancient Chinese mathematics</p>
</div></div></div>Can a Bicycle Create a Unicycle Track?
http://www.maa.org/programs/maa-awards/writing-awards/can-a-bicycle-create-a-unicycle-track
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b> George Pólya Award</p>
<p><b>Year of Award:</b> 2003</p>
<p><b>Publication Information:</b> <em>The College Mathematics Journal</em>, Vol. 33 (2002), pp. 283-292.</p>
<p><b>Summary:</b> The author argues that a bicycle can create a single (unicycle) track.</p>
<p><b><a href="/sites/default/files/pdf/upload_library/22/Polya/Finn.pdf">Read the article.</a></b></p></div></div></div>Conformality, the Exponential Function, and World Map Projections
http://www.maa.org/programs/maa-awards/writing-awards/conformality-the-exponential-function-and-world-map-projections
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b>George Pólya Award</p>
<p><b>Year of Award:</b> 2002</p>
<p><b>Publication Information:</b> <em>The College Mathematics Journal</em>, Vol. 32 (2001), pp. 334-342.</p>
<p><b>Summary:</b> In this paper the author uses single-variable calculus to establish the conformality of the stereographic projection and the Mercator world map.</p>
<p><b><a href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020799.02p0702q.pdf">Read the article.</a></b></p></div></div></div>Surface Area and the Cylinder Area Paradox
http://www.maa.org/programs/maa-awards/writing-awards/surface-area-and-the-cylinder-area-paradox
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b> George Pólya</p>
<p><b>Year of Award:</b> 1978</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 8, No. 4, (1977), pp. 207-211</p>
<p><b>Summary:</b> A discussion of H.A. Schwartz's cylinder area paradox that opened the floodgates of mathematical inquiry to investigations into surfaces and surface areas.</p>
<p><a href="/sites/default/files/pdf/upload_library/22/Polya/00494925.di020678.02p0385w.pdf" title="Read the Article">Read the Article</a></p></div></div></div>