Proposals
Below are some proposals for talks from the past (and current). By clicking on the ID number, more details are shown. By default, these are sorted chronologically (recent first) and by then by last name. The data can be sorted by alternate means by using the links at the top right, each allowing ascending or descending orders.
Displaying 1-20 of 471 results.
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ID:
40
Year: 2004
Name: a.m. fink
Institution:
Subject area(s):
Title of Talk: The effect of philosophy on curriculum
Abstract: I wrote a history of the Iowa State Mathematics Department and discovered that the curriculum offered was very dependent on outside influences and the philosophy of eductation of the those outside influences.
Year: 2004
Name: a.m. fink
Institution:
Subject area(s):
Title of Talk: The effect of philosophy on curriculum
Abstract: I wrote a history of the Iowa State Mathematics Department and discovered that the curriculum offered was very dependent on outside influences and the philosophy of eductation of the those outside influences.
ID:
109
Year: 2005
Name: Charles Ashbacher
Institution:
Subject area(s): Recreational mathematics
Title of Talk: Searching For Images Embedded in Mathematics
Abstract: In the science fiction book
Year: 2005
Name: Charles Ashbacher
Institution:
Subject area(s): Recreational mathematics
Title of Talk: Searching For Images Embedded in Mathematics
Abstract: In the science fiction book
ID:
133
Year: 2005
Name: Phil Wood
Institution:
Subject area(s): Calculus
Title of Talk: Simple Teaching of Differential Calculus
Abstract: Calculus may be taught more understandably by first describing its practical uses and then presenting it as simple algebra and geometry. In doing this all mention of infinitesimals, increments, theory of limits and formal proofs has been eliminated.
Year: 2005
Name: Phil Wood
Institution:
Subject area(s): Calculus
Title of Talk: Simple Teaching of Differential Calculus
Abstract: Calculus may be taught more understandably by first describing its practical uses and then presenting it as simple algebra and geometry. In doing this all mention of infinitesimals, increments, theory of limits and formal proofs has been eliminated.
ID:
262
Year: 2009
Name: Louis Kauffman
Institution: University of Illinois at Chicago
Subject area(s): MAA George Polya Lecturer
Title of Talk: Introduction to Knot Theory
Abstract: The theory of knots is a recent part of mathematics. It originated in the tabulation of tables of knots by the mathematicians Tait, Kirkman and Little in the 19th century. These tables were prepared at the behest of Lord Kelvin (Sir William Thompson) who had developed a theory that atoms were three dimensional knotted vortices in the luminiferous aether. Along with these speculations came the development of geometry and topology in the hands of Gauss, Riemann, Poincare and others. As the knotted vortex theory declined (it has never entirely disappeared!), the mathematics of topology ascended, and the theory of knots came into being as part of the study of low dimensional manifolds, using the fundamental group of Poincare and early versions of homology theory. Max Dehn used the fundamental group to show that a trefoil knot and its mirror image are topologically distinct. J. W. Alexander in the 1920's found a polynomial invariant of knots that bears his name to this day. Kurt Reidemeister, in the 1920's, discovered a set of moves on diagrams for knots that made their classification a (difficult) combinatorial problem. In the 1980's there came a rebirth of these combinatorial schemes in the discovery of the Jones polynomial invariant of knots and links (and its relatives and descendants). Along with the new combinatorial invariants came new relationships with physics and with many fields of mathematics (combinatorics, graph theory, Hopf algebras, Lie algebras, von Neumann algebras, functional integration, category theory) and new kinds of mathematics such as higher categories and categorification. This talk will discuss the history of knot theory and then it will concentrate on describing the Jones polynomial, its relationships with physics, and recent developments related to categorification.
Year: 2009
Name: Louis Kauffman
Institution: University of Illinois at Chicago
Subject area(s): MAA George Polya Lecturer
Title of Talk: Introduction to Knot Theory
Abstract: The theory of knots is a recent part of mathematics. It originated in the tabulation of tables of knots by the mathematicians Tait, Kirkman and Little in the 19th century. These tables were prepared at the behest of Lord Kelvin (Sir William Thompson) who had developed a theory that atoms were three dimensional knotted vortices in the luminiferous aether. Along with these speculations came the development of geometry and topology in the hands of Gauss, Riemann, Poincare and others. As the knotted vortex theory declined (it has never entirely disappeared!), the mathematics of topology ascended, and the theory of knots came into being as part of the study of low dimensional manifolds, using the fundamental group of Poincare and early versions of homology theory. Max Dehn used the fundamental group to show that a trefoil knot and its mirror image are topologically distinct. J. W. Alexander in the 1920's found a polynomial invariant of knots that bears his name to this day. Kurt Reidemeister, in the 1920's, discovered a set of moves on diagrams for knots that made their classification a (difficult) combinatorial problem. In the 1980's there came a rebirth of these combinatorial schemes in the discovery of the Jones polynomial invariant of knots and links (and its relatives and descendants). Along with the new combinatorial invariants came new relationships with physics and with many fields of mathematics (combinatorics, graph theory, Hopf algebras, Lie algebras, von Neumann algebras, functional integration, category theory) and new kinds of mathematics such as higher categories and categorification. This talk will discuss the history of knot theory and then it will concentrate on describing the Jones polynomial, its relationships with physics, and recent developments related to categorification.
ID:
396
Year: 2014
Name: Dave Renfro
Institution: #business/industry/government
Subject area(s): calculus, real analysis
Title of Talk: Calculus Curiosities
Abstract: Over the years I have collected a lot of little-known mathematical curiosities and minutia from various books and journal articles. This talk is intended to be a "show and tell" for some of this material, mostly restricted to things that could be of use in first year calculus courses, or at least to things likely to be of interest to teachers of such courses.
Year: 2014
Name: Dave Renfro
Institution: #business/industry/government
Subject area(s): calculus, real analysis
Title of Talk: Calculus Curiosities
Abstract: Over the years I have collected a lot of little-known mathematical curiosities and minutia from various books and journal articles. This talk is intended to be a "show and tell" for some of this material, mostly restricted to things that could be of use in first year calculus courses, or at least to things likely to be of interest to teachers of such courses.
ID:
318
Year: 2011
Name: David Bressoud
Institution: #non-IA section
Subject area(s):
Title of Talk: Issues of the Transition to College Mathematics
Abstract: Over the past quarter century, 2- and 4-year college enrollment in first semester calculus has remained constant while high school enrollment in calculus has grown tenfold, from 60,000 to 600,000, and continues to grow at 6% per year. We have passed the cross-over point where each year more students study first semester calculus in US high schools than in all 2- and 4-year colleges and universities in the United States. In theory, this should be an engine for directing more students toward careers in science, engineering, and mathematics. In fact, it is having the opposite effect. This talk will present what is known about the effects of this growth and what needs to happen in response within our high schools and universities.
Year: 2011
Name: David Bressoud
Institution: #non-IA section
Subject area(s):
Title of Talk: Issues of the Transition to College Mathematics
Abstract: Over the past quarter century, 2- and 4-year college enrollment in first semester calculus has remained constant while high school enrollment in calculus has grown tenfold, from 60,000 to 600,000, and continues to grow at 6% per year. We have passed the cross-over point where each year more students study first semester calculus in US high schools than in all 2- and 4-year colleges and universities in the United States. In theory, this should be an engine for directing more students toward careers in science, engineering, and mathematics. In fact, it is having the opposite effect. This talk will present what is known about the effects of this growth and what needs to happen in response within our high schools and universities.
ID:
321
Year: 2011
Name: David Bressoud
Institution: #non-IA section
Subject area(s):
Title of Talk: The Truth of Proofs
Abstract: Mathematicians often delude themselves into thinking that we create proofs in order to establish truth. In fact, that which is "proven" is often not true, and mathematical results are often known with certainty to be true long before a proof is found. I will use some illustrations from the history of mathematics to make this point and to show that proof is more about making connections than establishing truth.
Year: 2011
Name: David Bressoud
Institution: #non-IA section
Subject area(s):
Title of Talk: The Truth of Proofs
Abstract: Mathematicians often delude themselves into thinking that we create proofs in order to establish truth. In fact, that which is "proven" is often not true, and mathematical results are often known with certainty to be true long before a proof is found. I will use some illustrations from the history of mathematics to make this point and to show that proof is more about making connections than establishing truth.
ID:
177
Year: 2006
Name: Kenneth Driessel
Institution: #non-IA section
Subject area(s): classical mechanics, bio-mechanics
Title of Talk: The Dynamics of a Planar Two Link Chain and Some Applications to Human Motion
Abstract: Try the following 'acceleration experiment': Stand balanced with your legs straight and a slight forward bend at the waist. Then step backwards. Consider the following 'acceleration question': How do humans initiate this motion? Or more generally: How do humans usually initiate horizontal motion from a balanced position? (I first met this question when thinking about cross country skiing.) We analyze the acceleration question by analogy. In particular, we study the classical dynamics of a mechanical system consisting of two linked rods. We assume that the first rod is connected to the ground by a hinge. (The first rod corresponds to the human legs. The ground hinge corresponds to the human ankles.) We assume that the second rod is connected to the first one by another hinge. (The second rod corresponds to the human torso. The second hinge corresponds to the human hips.) We derive the equations of motion for this mechanical system. We prove that if the system is initially at rest in a balanced position then gravity causes the center of mass to accelerate in the horizontal direction toward which the system is 'pointed'. We infer that the step backwards in the acceleration experiment is initiated by a relaxation of the muscles at the hips. Reference: Kenneth R. Driessel and Irvin R. Hentzel, 'Dynamics of a Planar Two Link Chain', http://www.fiberpipe.net/~driessel/2-links.pdf
Year: 2006
Name: Kenneth Driessel
Institution: #non-IA section
Subject area(s): classical mechanics, bio-mechanics
Title of Talk: The Dynamics of a Planar Two Link Chain and Some Applications to Human Motion
Abstract: Try the following 'acceleration experiment': Stand balanced with your legs straight and a slight forward bend at the waist. Then step backwards. Consider the following 'acceleration question': How do humans initiate this motion? Or more generally: How do humans usually initiate horizontal motion from a balanced position? (I first met this question when thinking about cross country skiing.) We analyze the acceleration question by analogy. In particular, we study the classical dynamics of a mechanical system consisting of two linked rods. We assume that the first rod is connected to the ground by a hinge. (The first rod corresponds to the human legs. The ground hinge corresponds to the human ankles.) We assume that the second rod is connected to the first one by another hinge. (The second rod corresponds to the human torso. The second hinge corresponds to the human hips.) We derive the equations of motion for this mechanical system. We prove that if the system is initially at rest in a balanced position then gravity causes the center of mass to accelerate in the horizontal direction toward which the system is 'pointed'. We infer that the step backwards in the acceleration experiment is initiated by a relaxation of the muscles at the hips. Reference: Kenneth R. Driessel and Irvin R. Hentzel, 'Dynamics of a Planar Two Link Chain', http://www.fiberpipe.net/~driessel/2-links.pdf
ID:
290
Year: 2010
Name: Charles Ashbacher
Institution: #none
Subject area(s): Recreational mathematics
Title of Talk: Retrolife Generation of the Twelve Pentominoes
Abstract: The "Game of Life" invented by J. H. Conway has fascinated people for decades and was the impetus for the field of artificial life. Retrolife is determining if a specific pattern can be created from another with one iteration of the rules of life. This presentation will answer the question whether each of the twelve pentominoes can be generated via an iteration of the rules and poses new questions.
Year: 2010
Name: Charles Ashbacher
Institution: #none
Subject area(s): Recreational mathematics
Title of Talk: Retrolife Generation of the Twelve Pentominoes
Abstract: The "Game of Life" invented by J. H. Conway has fascinated people for decades and was the impetus for the field of artificial life. Retrolife is determining if a specific pattern can be created from another with one iteration of the rules of life. This presentation will answer the question whether each of the twelve pentominoes can be generated via an iteration of the rules and poses new questions.
ID:
308
Year: 2011
Name: Charles Ashbacher
Institution: #none
Subject area(s): Recreational mathematics
Title of Talk: A Simple Puzzle in Arithmetic Logic For Mathematical Exercise
Abstract: The KenKen is a simple math puzzle that was created by Tetsuya Miyamoto and is based on the operations of simple arithmetic on an n x n grid. The question of note is, how many puzzles are there up through the 9 x 9 grid?
Year: 2011
Name: Charles Ashbacher
Institution: #none
Subject area(s): Recreational mathematics
Title of Talk: A Simple Puzzle in Arithmetic Logic For Mathematical Exercise
Abstract: The KenKen is a simple math puzzle that was created by Tetsuya Miyamoto and is based on the operations of simple arithmetic on an n x n grid. The question of note is, how many puzzles are there up through the 9 x 9 grid?
ID:
317
Year: 2011
Name: Panel Discussants
Institution: #none
Subject area(s):
Title of Talk: Developments in Calculus Instruction
Abstract: All Special Session Speakers, along with representatives from several other institutions in the Section, will discuss and entertain questions about current and impending developments.
Year: 2011
Name: Panel Discussants
Institution: #none
Subject area(s):
Title of Talk: Developments in Calculus Instruction
Abstract: All Special Session Speakers, along with representatives from several other institutions in the Section, will discuss and entertain questions about current and impending developments.
ID:
332
Year: 2012
Name: Charles Ashbacher
Institution: #none
Subject area(s): Teaching of statistics
Title of Talk: Bayes' Theorem in the Modern World
Abstract: Despite having been repeatedly debunked, the idea of testing all members of a population for a characteristic a small percentage has continues to appear in our political world. The foolishness of this is easily demonstrated by applying Bayes
Year: 2012
Name: Charles Ashbacher
Institution: #none
Subject area(s): Teaching of statistics
Title of Talk: Bayes' Theorem in the Modern World
Abstract: Despite having been repeatedly debunked, the idea of testing all members of a population for a characteristic a small percentage has continues to appear in our political world. The foolishness of this is easily demonstrated by applying Bayes
ID:
181
Year: 2007
Name: Charles Ashbacher
Institution: #none
Subject area(s):
Title of Talk: Computer Explorations of Prime Conjectures Made by Marnell
Abstract: In 1742, Goldbach made a conjecture that every even integer greater than 2 is expressible as the sum of two primes. While extensive computer searches have failed to find a counterexample, the general conjecture remains open, although nearly everyone believes that it is true. In a recent submission to Journal of Recreational Mathematics, Geoffrey Marnell made ten additional conjectures regarding what can be expressed using prime numbers. This paper gives the results of computer explorations carried out to test the conjectures.
Year: 2007
Name: Charles Ashbacher
Institution: #none
Subject area(s):
Title of Talk: Computer Explorations of Prime Conjectures Made by Marnell
Abstract: In 1742, Goldbach made a conjecture that every even integer greater than 2 is expressible as the sum of two primes. While extensive computer searches have failed to find a counterexample, the general conjecture remains open, although nearly everyone believes that it is true. In a recent submission to Journal of Recreational Mathematics, Geoffrey Marnell made ten additional conjectures regarding what can be expressed using prime numbers. This paper gives the results of computer explorations carried out to test the conjectures.
ID:
223
Year: 2008
Name: Charles Ashbacher
Institution: #none
Subject area(s): Recreational mathematics
Title of Talk: Computer Investigations of Problems in Pickover
Abstract: Clifford Pickover, who has been described as the
Year: 2008
Name: Charles Ashbacher
Institution: #none
Subject area(s): Recreational mathematics
Title of Talk: Computer Investigations of Problems in Pickover
Abstract: Clifford Pickover, who has been described as the
ID:
144
Year: 2006
Name: Dave L. Renfro
Institution: ACT Inc.
Subject area(s): transcendental equations
Title of Talk: The Remarkable Equation tan(x) = x
Abstract: Although tan(x) = x is virtually the prototypical example for solving an equation by graphical methods, and this equation frequently appears in calculus texts as an example of Newton's method, there seems to be nothing in the literature that surveys what is known about its solutions. In this talk I will look at some appearances of this equation in elementary calculus, some appearances of this equation in more advanced areas (quantum mechanics, heat conduction, etc.), the fact that this equation has no nonreal solutions and that all of its nonzero solutions are transcendental, and some curious infinite sums involving its solutions. In addition, I will discuss some of the history behind this equation, including contributions by Euler (1748), Fourier (1807), Cauchy (1827), and Rayleigh (1874, 1877).
Year: 2006
Name: Dave L. Renfro
Institution: ACT Inc.
Subject area(s): transcendental equations
Title of Talk: The Remarkable Equation tan(x) = x
Abstract: Although tan(x) = x is virtually the prototypical example for solving an equation by graphical methods, and this equation frequently appears in calculus texts as an example of Newton's method, there seems to be nothing in the literature that surveys what is known about its solutions. In this talk I will look at some appearances of this equation in elementary calculus, some appearances of this equation in more advanced areas (quantum mechanics, heat conduction, etc.), the fact that this equation has no nonreal solutions and that all of its nonzero solutions are transcendental, and some curious infinite sums involving its solutions. In addition, I will discuss some of the history behind this equation, including contributions by Euler (1748), Fourier (1807), Cauchy (1827), and Rayleigh (1874, 1877).
ID:
370
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
ID:
371
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
ID:
516
Year: 2018
Name: Carlos Castillo-Chavez
Institution: Arizona State University
Subject area(s):
Title of Talk: Epidemiology: Role of dynamic individual decisions during ongoing epidemic outbreaks
Abstract: The lecture begins with a historical review of epidemic models and the concept of tipping point. We then revisit phenomenologically inspired modeling frameworks that account for the impact that single disease outbreaks have on the decisions that individuals make in response to real or perceived risk of infection. Finally, a behavioral framework where individual decisions are modeled as a function of tradeoffs made in response to self-assessed costs tied to present or future risks of infection, including those resulting from potential loss of benefits due to risk aversion decisions is introduced and implemented on a simplified population-level epidemic model. The impact of these decisions is illustrated in the context of a single influenza outbreak.
Year: 2018
Name: Carlos Castillo-Chavez
Institution: Arizona State University
Subject area(s):
Title of Talk: Epidemiology: Role of dynamic individual decisions during ongoing epidemic outbreaks
Abstract: The lecture begins with a historical review of epidemic models and the concept of tipping point. We then revisit phenomenologically inspired modeling frameworks that account for the impact that single disease outbreaks have on the decisions that individuals make in response to real or perceived risk of infection. Finally, a behavioral framework where individual decisions are modeled as a function of tradeoffs made in response to self-assessed costs tied to present or future risks of infection, including those resulting from potential loss of benefits due to risk aversion decisions is introduced and implemented on a simplified population-level epidemic model. The impact of these decisions is illustrated in the context of a single influenza outbreak.
ID:
511
Year: 2018
Name: Lindsay Erickson
Institution: Augustana University
Subject area(s): Graph Theory, Game Theory
Title of Talk: Edge-Nim on the $K_{2,n}$
Abstract: Edge-Nim is a combinatorial game played on finite regular graphs with positive, integrally weighted edges. Two players alternately begin from an initialized vertex and move to an adjacent vertex, decreasing the weight of the incident edge to a strictly non-negative integer as they travel across it. The game ends when a player is confronted by a position where no incident edge has a nonzero weight (or, that is to say, when the player is unable to move), in which case, this player loses. We characterize the winner of edge-Nim on the complete bipartite graphs, $K_{2,n}$ for all positive integers, $n$, giving the solution and complete strategy for the player able to win.
Year: 2018
Name: Lindsay Erickson
Institution: Augustana University
Subject area(s): Graph Theory, Game Theory
Title of Talk: Edge-Nim on the $K_{2,n}$
Abstract: Edge-Nim is a combinatorial game played on finite regular graphs with positive, integrally weighted edges. Two players alternately begin from an initialized vertex and move to an adjacent vertex, decreasing the weight of the incident edge to a strictly non-negative integer as they travel across it. The game ends when a player is confronted by a position where no incident edge has a nonzero weight (or, that is to say, when the player is unable to move), in which case, this player loses. We characterize the winner of edge-Nim on the complete bipartite graphs, $K_{2,n}$ for all positive integers, $n$, giving the solution and complete strategy for the player able to win.
ID:
568
Year: 2021
Name: José Contreras
Institution: Ball State University
Subject area(s): Geometry
Title of Talk: The Power of GeoGebra to Investigate Converse Problems
Abstract: In this presentation, I illustrate how my students and I use GeoGebra to explore geometric converse problems. In particular, we use GeoGebra to gain insight into the solution to the following three problems: 1) Let ABCD be a quadrilateral with medial quadrilateral EFGH. If EFGH is a rectangle, what type of quadrilateral is ABCD? 2) Let E, F, G, and H be the midpoints of the consecutive sides of a quadrilateral ABCD. If EFGH is a rhombus, characterize quadrilateral ABCD. 3) E, F, G, and H are the midpoints of the consecutive sides of a quadrilateral ABCD. Name quadrilateral ABCD when EFGH is a square.
Year: 2021
Name: José Contreras
Institution: Ball State University
Subject area(s): Geometry
Title of Talk: The Power of GeoGebra to Investigate Converse Problems
Abstract: In this presentation, I illustrate how my students and I use GeoGebra to explore geometric converse problems. In particular, we use GeoGebra to gain insight into the solution to the following three problems: 1) Let ABCD be a quadrilateral with medial quadrilateral EFGH. If EFGH is a rectangle, what type of quadrilateral is ABCD? 2) Let E, F, G, and H be the midpoints of the consecutive sides of a quadrilateral ABCD. If EFGH is a rhombus, characterize quadrilateral ABCD. 3) E, F, G, and H are the midpoints of the consecutive sides of a quadrilateral ABCD. Name quadrilateral ABCD when EFGH is a square.