Do Dogs Know Calculus?

Pennings, Timothy J.

doi:10.1080/07468342.2003.11922003

Cited by 19 publications

(15 citation statements)

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“…Our perspective is that the decision maker does something analogous to the computations specified in the model equation. Utilities come to mind as if they were explicitly calculated using the MAU equation, just as a predator finds an optimal path toward moving prey as though using calculus (Pennings 2003). Hoffman (1960) refers to this kind of model as "paramorphic," conveying the idea of structural similarity.…”

Section: Discussionmentioning

confidence: 99%

A descriptive multi-attribute utility model for everyday decisions

Weiss

Edwards

2009

Theory Decis

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Section: Discussionmentioning

confidence: 99%

A descriptive multi-attribute utility model for everyday decisions

Weiss

Edwards

2009

Theory Decis

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“…[3] and "Do Dogs Know Related Rates Rather Than Optimization?" [4], both published in the College Mathematics Journal.…”

Section: Background Informationmentioning

confidence: 99%

“…Of course, wheelbarrow racing cannot be completely avoided; each group must do at least 66 meters of wheelbarrow racing, which is slow and somewhat painful. Following the derivation in [3], if we let y be the amount of time it takes to complete this race given a sack race speed of s, a wheelbarrow speed of w, sack racing from (102, 0) to (x, 0) and wheelbarrow racing from (x, 0) to (0, 66), we get (4):…”

Section: Background Informationmentioning

confidence: 99%

“…The second project is a human take on the popular article "Do Dogs Know Calculus?" [3]. These projects take interactivity to new levels in mathematics courses by actually requiring the students to engage in physical activity to generate the facts that they will analyze using calculus, while also presenting students with a life lesson to take with them after the course.…”

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Sharks, Minnows, and Wheelbarrows: Calculus Modeling Projects

Smith¹

2011

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The purpose of this article is to present two very active applied modeling projects that were successfully implemented in a first semester calculus course at Hollins University. The first project uses a logistic equation to model the spread of a new disease such as swine flu. The second project is a human take on the popular article "Do Dogs Know Calculus?" [3]. These projects take interactivity to new levels in mathematics courses by actually requiring the students to engage in physical activity to generate the facts that they will analyze using calculus, while also presenting students with a life lesson to take with them after the course. The benefits that students get from these projects outweigh the loss of the small amount of lecture time required to collect the necessary data.

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“…However, Pennings demonstrated that even without doing calculations the dogs chose a near optimal path for when to stop running and jump in the water and swim in order to minimize the time required to reach a ball floating in the waters of Lake Michigan [9]. This article is relevant because it demonstrates an example in which animals with no knowledge of calculus acted in an optimal way.…”

Section: Dogs Optimizationmentioning

confidence: 99%

Using Biomechanical Optimization To Interpret Dancers' Pose Selection For A Partnered Spin

Selbach-Allen¹

2009

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) AND ADDRESS(ES) PERFORMING ORGANIZATION REPORT NUMBER SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)U.S. Naval Academy Annapolis, MD 21402 SPONSOR/MONITOR'S REPORT NUMBER(S)Trident Scholar Project Report no. 382 (2009) DISTRIBUTION / AVAILABILITY STATEMENTThis document has been approved for public release; its distribution is UNLIMITED SUPPLEMENTARY NOTES ABSTRACTOur goal was to determine whether expert swing dancers physically optimize their pose for a partnered spin. In a partnered spin, two dancers connect hands and spin around a single vertical axis. We describe the pose of a couple by the angles of their joints in a twodimensional plane. These angles were outputs of an optimization model that gave the ideal pose for a couple. A biomechanical model built in Mathematica allowed comparisons to live dancers with the use of a motion capture system. SUBJECT TERMS AbstractOur goal was to determine whether expert swing dancers physically optimize their pose for a partnered spin. In a partnered spin, two dancers connect hands and spin around a single vertical axis. We describe the pose of a couple by the angles of their joints in a two-dimensional plane. These angles were outputs of an optimization model that gave the ideal pose for a couple. A biomechanical model built in Mathematica allowed comparisons to live dancers with the use of a motion capture system.The optimization objective is to maximize angular acceleration, by minimizing the resistance to spin, but still producing torque. The model considers only external forces and neglects internal forces. It consists of equations derived from physical principles such as Newton's laws and moment of inertia calculations that govern how people move. Using numerical non-linear optimization we found the pose for each couple that maximizes their angular acceleration. Different dancers are differently sized, so every couple has a different optimal pose. Each couple's optimal pose was compared to the pose they actually assumed for the spin.Our motion capture system consisted of four video cameras, reflective balls that could be tracked, and software to integrate the different angles of the cameras. The captured data consisted of the three-dimensional location of each of the marked body joints. We used this data to determine the angles of the joints to calculate the couple's actual pose. The couple's actual pose was used to calculate a predicted angular acceleration. Thi...

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Do Dogs Know Calculus?

Cited by 19 publications

References 0 publications

A descriptive multi-attribute utility model for everyday decisions

A descriptive multi-attribute utility model for everyday decisions

Sharks, Minnows, and Wheelbarrows: Calculus Modeling Projects

Using Biomechanical Optimization To Interpret Dancers' Pose Selection For A Partnered Spin

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