The dog’s choice of route was confirmed by calculus-based maths to be consistently the most expedient. Taking into account the various required angles and distances of running on the beach sand (quicker) or swimming through the water (slower), and at which point these variables were most efficiently utilised, Elvis could expedite retrieval. He discovered that if he threw a ball into the sea, Elvis was able to calculate the shortest route to retrieve it. Mathematician TJ Pennings has written a paper on his dog Elvis’s use of calculus. His discovery has received international media attention.Prof Pennings published his findings in a (now popular) research paper: Do Dogs Know Calculus? TJ Pennings, The College Mathematics Journal, Volume 34, No 3 (May, 2003), pp 178-182.By using calculus, Prof Pennings was able to show that Elvis almost always took a path that was close to the optimal solution (he computed the optimal path after performing various measurements of distances and speed).Curiously, Elvis took the path that minimised the time it took to reach the ball!.Instead, Elvis ran part of the way along the beach, and then at some mystery point he plunged into the water swimming diagonally to the ball (illustrated by the green line) One possible path was for Elvis to simply jump into the water and swim directly to the ball (illustrated by the red line) Such a path minimised distance to the ball.īut if Elvis didn’t like the water, he might have sprinted down the beach to the point on shore closest to the ball and then turned at a right angle and swim to the ball (illustrated by the blue line) He took Elvis to the beach and threw a ball into the water The rider sits at the origin and faces toward. The downward-bending parts may be viewed as 'places for legs.' A standard mathematical model is the graph z x2 y2 z x 2 y 2. In 2003, Tim Pennings (an associate professor at Hope College) performed an experiment with his Corgi named Elvis tl dr: A saddle is a surface resembling a removable seat for horseback riding, which bends downward on the sides and upward to the front and back of the rider. It is part of modern mathematics education. What is calculus? Calculus is the study of change, in the same way that geometry is the study of shape.
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