Assignments:

Applets

Sources/Resources

Original Applets

Infinity Podcast


Applet Collections


Title Description
Rossman/Chance Applet Collection This collection of applets is specific to statistics, and offers aid in areas ranging from probability to statistical inference.
Wolfram Demonstrations Project This collection has a range of applets from mathematics, to art, to the physical sciences! The mathematics portion has applets for the high school level, as well as many other interesting mathematical topics.
Project Interactivate A site with applets for subjects in Algebra, Calculus, Discrete, Geometry, Probability, Statistics, etc. The collections allows you to search by subject or by grade level, ranging from 3rd grade to undergraduate.
Apps on Mathematics This collection created by Walter Fendt has a variety of applets in the areas of arithmetic and geometry. They are all used with HTML5, so there are no problems with java.
Saltaire Software This site has many applets specific to geometry; from simple to advanced.
Calculus Applets - Geogebra Here is a large collection of Calculus related Geogebra applets; they range from derivatives and integrals, to differential equations and series.


Infinity Applets


Title Description
Riemann Sums This applet helps to visualize how Riemann sums can approximate the area under a curve. The user can see that, as the number of rectangles approaches infinity, the sum approaches the actual area.
Infinite Series This program helps visualize how we can use infinite series to approximate famous mathematical constants.
Sum of Infinite Geometric Series This applet allows you to visualize the sum of an infinite, geometric series as you add terms to the series and change the common ratio in the series.
Limits at Infinity This Geogebra outlet lets the user visualize how some values approach infinity in some piecewise functions and functions with asymptotes.
Riemann Sums Cont. Here is another Geogebra applet for visualizing how Riemann sums approximate the area under a curve.
Baravelle's Spiral This applet uses Baravelle's Spiral to visualize the sum of an infinite geometric sequence.

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Resources (for Infinity project)


Resource Title Address
Video The Infinite Hotel Paradox https://www.youtube.com/watch?v=Uj3_KqkI9Zo
Website Math is Fun - Infinity https://www.mathsisfun.com/numbers/infinity.html
Podcast Infinity + One https://www.stufftoblowyourmind.com/podcasts/infinity-plus-one.htm
Podcast The Infinity Hotel https://www.stufftoblowyourmind.com/podcasts/the-infinity-hotel.htm
Video Proof some infinities are bigger than other infinities https://www.khanacademy.org/math/math-for-fun-and-glory/vi-hart/infinity/v/proof-infinities
Blog Infinity is NOT a number http://scienceblogs.com/goodmath/2008/10/13/infinity-is-not-a-number/
Applet Tortoise and Hare Race (Zeno's Paradox) http://www.shodor.org/interactivate/activities/Tortoise/
Website Zeno’s Paradox: Understanding Convergent & Divergent Series https://www.livescience.com/45253-zenos-paradox.html
Video Infinite Series as Limit of Partial Sums https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-1/v/infinite-series-as-limit-of-partial-sums
Website How to have Mind-Boggling Fun with Infinity https://boingboing.net/2015/01/07/how-to-have-mind-boggling-fun.html

Sources (for Infinity project)


Source Title Citation
Book The Mystery of the Aleph Aczel, A. D. (2000). The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity. New York, NY: Four Walls Eight Windows.
Article Dispute over Infinity Divides Mathematicians Wolchover, N. (2013, December 03). Dispute over Infinity Divides Mathematicians. Retrieved September 24, 2018, from https://www.scientificamerican.com/article/infinity-logic-law/
Website 19th Century Mathematics - Cantor Cantor - 19th Century Mathematics - The Story of Mathematics. (n.d.). Retrieved September 24, 2018, from https://www.storyofmathematics.com/19th_cantor.html
Journal Article Definition of Infinity Expands for Scientists and Mathematicians Begley, S. (2005, Jul 29). Definition of infinity expands for scientists and mathematicians. Wall Street Journal Retrieved from https://login.dist.lib.usu.edu/login?url=https://search-proquest-com.dist.lib.usu.edu/docview/398944612?accountid=14761
Journal Article Are all Infinities Created Equal? Paoletti, T. J. (2013). Are All Infinities Created Equal? Mathematics Teacher, 107(2), 98–103. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=asn&AN=90042315&site=ehost-live
Book Roads to Infinity Stillwell, J. C. (2010). Roads to infinity: the mathematics of truth and proof. AK Peters/CRC Press.
Journal Article Does Infinity come in Different Sizes? Matson, J. (2008). Does Infinity Come in Different Sizes? Scientific American, 298(1), 112. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=asn&AN=27818324&site=ehost-live
Magazine Article To Settle Infinity Dispute, a New Law of Logic Wolchover, B. (2013, November 26). To Settle Infinity Question, a New Law of Mathematics. Retrieved September 25, 2018, from https://www.quantamagazine.org/to-settle-infinity-question-a-new-law-of-mathematics-20131126/
Journal Article Towards a Biography of Georg Cantor I. Grattan-Guinness M.A. M.Sc. Ph.D. (1971) Towards a biography of Georg Cantor, Annals of Science, 27:4, 345-391, DOI: 10.1080/00033797100203837
Journal Article Methods for the Summation of Infinite Series Stenlund, H. (2016). Methods for the Summation of Infinite Series. International Journal of Mathematics & Computer Science, 11(2), 109–131. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=asn&AN=119398858&site=ehost-live
Journal Article Favorite mathematics topics from the 12th Century to the 21st Century Ghusayni, B. (2018). Favorite mathematics topics from the 12th Century to the 21st Century. International Journal of Mathematics & Computer Science, 13(1), 83–104. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=asn&AN=127054609&site=ehost-live
University Publication Cantor's Continuum Problem Criste, C. (2015). Cantor’s Continuum Problem. Yearbook of George Baritiu Institute of History in Cluj-Napoca, Series Humanistica, 13, 177–193. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=asn&AN=111993652&site=ehost-live
Journal Article Set Theory from Cantor to Cohen Kanamori, A. (2009). Set Theory From Cantor To Cohen. Philosophy of Mathematics, 395-459. doi:10.1016/b978-0-444-51555-1.50014-6
Journal Article Logic of Actual Infinity and G. Cantor's Diagonal Proof of the Uncountability of the Continuum Zenkin, A. (2003-2004). Logic of Actual Infinity and G. Cantor's Diagonal Proof of the Uncountability of the Continuum. The Review of Modern Logic, 9(3-4),27-82. Retrieved from https://projecteuclid.org/download/pdf_1/euclid.rml/1203431978
Journal Article The chicken went into the bush and never came back: a note on infinity Rauff, J. (2013). The chicken went into the bush and never came back: a note on infinity. BSHM Bulletin: Journal of the British Society for the History of Mathematics, 28(2), 97–100. https://doi-org.dist.lib.usu.edu/10.1080/17498430.2013.727147


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Original Applets


Title Description
Sine Transformations This applet shows how changing the values of A and B will change the function f(x)=Asin(Bx).
Conic Sections in 3D Space This applet allows the user to manipulate the different conic sections in a 3-Dimensional Plane.
Rectangular and Polar Coordinates This applet show the relationship between rectangular and polar coordinates.
Volumes of Spheres, Cones and Cylinders This applet helps the user discover the relationship between the volumes of spheres, cones and cylinders.
Upper and Lower Sums This applet investigates upper and lower sums in comparison to the actual area under a curve.
Normal Approximation to the Binomial This applet investigates the normal approximation to a binomial distribution.
Area of a Circle: Using Triangles This applet allows the user to investigate a method of approximating the area of a circle.
Power Series Expansion This applet explores the power series expansions for different functions.
Discovering the Formula for the Area of a Circle This applet leads the user to discover where the formula for the area of a circle actually comes from.


What is Infinity? : Podcast on Infinity
(Podcast Script)

"We should read that as "the limit as x becomes infinite," not as "x approaches infinity" because again, infinity is neither a number nor a place."

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