Integration
http://www.maa.org/taxonomy/term/41616/0
enArc Length and Pythagorean Triples
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/arc-length-and-pythagorean-triples
<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>A family of curves whose lengths are closely related to Pythagorean Triples and therefore rational</em></p>
</div></div></div>The Fresnel Integrals Revisited
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-fresnel-integrals-revisited
<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>Without using double integrals, a new method is presented to evaluate the two Fresnel integrals about sine and cosine that has a wider applications than previous methods.</em></p>
</div></div></div>Complementary Coffee Cups
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/complementary-coffee-cups
<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>This capsule started with two coffee cups that are complementary, i.e., their profiles fit together. The author then explores the condition in which the two cups, obtained as solids of revolution, have the same volume. </em></p>
</div></div></div>Two Surprising Theorems on Cavalieri Congruence
http://www.maa.org/programs/maa-awards/writing-awards/two-surprising-theorems-on-cavalieri-congruence
<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> 1992</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 22, No. 2, (1991), pp. 118-124</p>
<p><b>Summary:</b> Discusses Cavlieri's early seventeenth century work on the "method of indivisibles," and applies Cavlieri's principles to produce two unexpected results.</p>
<p><a title="Read the Article" href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020746.02p00037.pdf">Read the Article</a></p></div></div></div>Inverse Problems and Torricelli's Law
http://www.maa.org/programs/maa-awards/writing-awards/inverse-problems-and-torricellis-law
<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> 1994</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 24, No. 3, (1993), pp. 210-217</p>
<p><b>Summary:</b> Three elementary inverse problems stemming from Torricelli's law which can be used to introduce undergraduates to notions related to ill-posed problems.</p>
<p><a title="Read the Article" href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020757.02p00026.pdf">Read the Article</a></p></div></div></div>Taking Limits Under the Integral Sign
http://www.maa.org/programs/maa-awards/writing-awards/taking-limits-under-the-integral-sign
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"><strong>Year of Award</strong>: 1968</p>
<p class="MsoNormal"><strong>Publication Information:</strong> <em>Mathematics Magazine,</em> vol. 40, 1967, pp. 179-186</p></div></div></div>Integrals Don't Have Anything to Do with Discrete Math, Do They?
http://www.maa.org/programs/maa-awards/writing-awards/george-polya-awards/integrals-dont-have-anything-to-do-with-discrete-math-do-they
<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>Year of Award:</strong> 2012</p>
<p><strong>Award:</strong> Allendoerfer</p>
<p><strong>Publication Information:</strong> <em>Mathematics Magazine</em>, vol. 84, 2011, pp. 108-119</p></div></div></div>Kepler: The Volume of a Wine Barrel - The Wine Barrel Incident
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-the-wine-barrel-incident
<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 his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</p>
</div></div></div>Kepler: The Volume of a Wine Barrel - Kepler's [i]Nova stereometria doliorum vinariorum[/i]
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-keplers-inova-stereometria-doliorum-vinariorumi
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</div></div></div>Kepler: The Volume of a Wine Barrel - Solving the Problem of Maxima: Wine Barrel Design
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-solving-the-problem-of-maxima-wine-barrel-design
<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 his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</p>
</div></div></div>Kepler: The Volume of a Wine Barrel - Kepler's Era
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-keplers-era
<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 his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</p>
</div></div></div>Kepler: The Volume of a Wine Barrel - Introduction
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel-introduction
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</div></div></div>Kepler: The Volume of a Wine Barrel
http://www.maa.org/press/periodicals/convergence/kepler-the-volume-of-a-wine-barrel
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.</div></div></div>Teaching the Fundamental Theorem of Calculus: A Historical Reflection - Concluding Remarks: The Relation between the History of Mathematics and Mathematics Education
http://www.maa.org/press/periodicals/convergence/teaching-the-fundamental-theorem-of-calculus-a-historical-reflection-concluding-remarks-the-relation
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">An argument that the teaching of elementary integration should better reflect its historical development</div></div></div>Area from Hand-Drawn Functions
http://www.maa.org/press/periodicals/loci/resources/area-from-hand-drawn-functions
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">The "area function" is often discussed as part of an introduction to the definite integral. This applet provides an innovative approach to producing functions drawn with a mouse in the context of an exploration/demonstration of the area function.</div></div></div>