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It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain. ...?

Kristi Hammond

in Physics

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Jodi Brooks on January 30, 2019


As far as I understand, this is the Pythagorean theorem in action. This theorem is widely used in baseball, so I’m not surprised you’ve gotten such an interesting question. When translated to bases and home plates, it becomes a bit confusing, to say the least, as you would hardly imagine geometry through sports.

As you should know, Pythagorean theorem explains the fundamental relation between three sides of a right triangle. When applied to baseball, it shows that the famous baseball diamond is actually a square with all sides being equal. The famous a² + b² = c² can resolve many equations of this sports gameplay.

Also, you may have heard about the relation of the Pythagorean theorem to calculate a team’s winning percentage. It is based on the belief that the actual winning percentage a team has does not represent its real performance. Instead, the right way to calculate it is to compare runs scored to runs allowed. There is an actual formula known as Pythagorean Winning Percentage that is widely used with the added exponent for more accuracy: W%=[(Runs Scored)^1.81]/[(Runs Scored)^1.81 + (Runs Allowed)^1.81]

This formula was created by Bill James, a baseball strategist. There is also an alternative formula suggested by a mathematician Stanley Rothman:
EXP(W%) = m* (RS - RA) + b

Where b is a constant that equal 0.50 and m is calculated based on all the results from 1998 to 2013.


Jeffrey Rodriguez on November 25, 2018

The answer is to Convert this into a geometry of the problem forces us to name the points. We will give the home plate of a symbol, the first base will be B, the second base is C, and the third base will be D. Now, we can present a geometric demonstration: STATEMENTS | REASONS (1) BC = CD | Given m(2) AC = AC | Reflexive Property (3) the triangle ACD = triangle ACB | SAS Congruence (4) AD = AB | CPCTC when CPCTC means Congruent parts of congruent Triangles are congruent. Therefore, the distance from first base to home plate, and from home plate to the third plate are equal.


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