Step 1: Read the article
Preview the questions below and read the article “Do Dogs Know Calculus?
Download Do Dogs Know Calculus?
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Use the link to load the article in a separate tab for ease of reference.
You do not need to work through the mathematics but you should understand the article.
You can skip the following parts of the document:
The first page of the document
The part on the last page of the document about “Rational Boxes.”
Step 2: Initial Post
To the extent that you are comfortable sharing with the class, reply to this discussion including BOTH listed items below. See How do I reply to a discussion as a student?
(Links to an external site.)
Address any ONE of the following “math content” prompts:
Explain the 4 “optimal path” options that the author considered. State each in the form “Maximize (or minimize) objective.” Which one did the author ultimately choose to evaluate?
For those familiar with statistics: Identify the statistical tools used and how they are applied.
For the “lab” student: Summarize the 4 simplifying assumptions made.
Address any ONE of the following “personal” prompts:
Discuss your ability to read, understand, and write about this article after learning about optimization in our class. Be specific about the parts of the article that might have confused you before our class.
Explain how analyzing this article might change the way you view course content and its potential application outside the classroom.
Describe a situation in which you have wondered about an optimization. Be sure to identify the objective quantity and whether the goal was to maximize or minimize it.
For the “lab” student: Summarize an experiment or another mathematical model you have encountered and the simplifying assumptions involved.
3. Optional, Make-up Prompt: If you miss part of either of the above prompts or a reply, you can earn back a point in advance by answering the question “What did you enjoy in the article?”
Post Format: Number your post with 1, 2, 3 (if applicable). After each number, paste the question you are responding to and then type your response.
For example how do the work :
The article “Do Dogs Know Calculus?” by Timothy J. Pennings presents an engaging exploration of whether a dog, specifically the author’s Welsh Corgi named Elvis, utilizes calculus principles to optimize its path when retrieving a tennis ball thrown into the water. This analysis is a classic calculus problem of finding the optimal path, in this case, to minimize retrieval time, a concept that many students encounter in their studies.
Minimize Distance Traveled: Elvis could immediately jump into the water and swim directly to the ball.
Minimize Swimming Distance: Elvis could run along the beach to the point closest to the ball before swimming, maximizing his running distance and minimizing his swim.
Hybrid Approach: Elvis runs a portion of the distance on the beach and then swims diagonally to the ball. This strategy involves finding a balance between running and swimming.
Run Entirely on Beach to Closest Point and then Swim: This option involves Elvis running to the point on the shore directly across from the ball before swimming, which is similar to option 2
My comprehension and enjoyment of Timothy J. Pennings’ essay “Do Dogs Know Calculus?” has much enhanced since we studied optimization in calculus class. Calculus applied to a dog’s fetching technique may have sounded abstract at first. It would have been difficult to understand the topic of optimizing Elvis the dog’s route to reduce retrieve time without a foundation in optimization concepts. It would have been unclear before this lesson how to apply the Harris-Benedict equation in practice to determine Basal Metabolic Rate (BMR) and how it relates to behavior optimization. Having gained a stronger comprehension of optimization, I am now able to appreciate how the essay uses mathematics to explain natural actions, such as Elvis’s intuitive decision to take the most efficient route. This understanding has improved my ability to interact with the material and have discussions about it, demonstrating to me the usefulness of calculus in both the natural world and daily life. My understanding of this topic has grown as a result of realizing how widely mathematical ideas may be used outside of theoretical problems.
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