Math Homework: Pythagoras Theorem and Baseball Field Analysis

This homework assignment explores the application of the Pythagoras theorem, a fundamental concept in mathematics, using a baseball field as a practical example. The assignment discusses the theorem's relevance to right-angled triangles and how it can be applied to calculate distances within the baseball diamond. Furthermore, the assignment delves into the comparison between problem-based and activity-based learning approaches, supported by a survey conducted with 12 participants. The results of the survey, presented in tabular form, indicate a preference for structured exercises over activity-based learning, suggesting that participants find clarity through solving exercises. The conclusion emphasizes the importance of a solid understanding of the subject matter before applying the concepts through activities.

Running Head: PYTHAGORAS THEOREM AND BASEBALL FIELD
Pythagoras Theorem and Baseball Field
Name of the Student
Name of the University
Author Note

1PYTHAGORAS THEOREM AND BASEBALL FIELD
Abstract
In this study, discussion will be conducted on problem based learning and activity based
learning. An example of the application of Pythagoras theorem in the baseball field have been
discussed. It has been seen from analysis performed that people prefer the problem based
learning more than activity based learning.

2PYTHAGORAS THEOREM AND BASEBALL FIELD
Introduction
This paper is mainly made on the opinions on problem based and activity based
learning. To understand which is a more efficient method of learning, an example has been
considered. Pythagoras theorem is one of the most important topics that is taught in
mathematics. Pythagoras theorem can also be applied in a baseball game. The relationship
will be discussed and the opinion of people on the two approaches will also be discussed.
Background
Pythagoras theorem is mainly applied to right angled triangles. In the following
figure, it can be seen that the lengths of the three sides of a triangle are a, b and c, where c is
the largest side known as the hypotenuse. According to the Pythagoras theorem, a2 + b2 = c2.
This is theory that is generally taught in schools.
Figure 1: Right angled triangle
Now, considering a baseball field given in figure 2, the shape of the infield is a
diamond. The distance between each of the three bases and the home plate are 90 feet and
form right angles. Using the Pythagoras theorem, it can be found out, how far the second
baseman has to throw the ball in order to get the runner out before he slides into the home
plate.

3PYTHAGORAS THEOREM AND BASEBALL FIELD
Figure 2: Baseball Field
Study
12 participants were selected randomly from a locality and they were asked the
questions attached in the appendix section. Each of the 12 participants have shared their
views on how they have been taught in schools. The results of the survey is discussed in the
following section.
Results
It can be seen from the analysis that most of the selected participants are less than 20
years old. From the table of the gender of the participants, it can be seen that there are equal
number of male and female candidates who have given their opinions of the matter.
From the table 3, it can be seen that most of the respondents have learned
mathematics as taught by the teacher in the class and then by solving exercises. Activity
based learning has not been adopted.
From table 4, it can be seen that most of the people have learned chemistry as taught
by the teacher in the class and then by solving exercises. Activity based learning has not been
adopted.

4PYTHAGORAS THEOREM AND BASEBALL FIELD
From table 5, it can be seen that most of the people have learned art as taught by the
teacher in the class and then by solving exercises. Activity based learning has not been
adopted.
From table 6, it can be seen that most of the people neither agree or disagree to the
fact that problem based learning is hard for less able people. Table 7 shows that an equal
number of people neither agree nor disagree too the fact that problem-based learning takes a
lot longer, and so is less efficient, than traditional classroom learning. From table 8, it can be
seen that the disagreement of the people are higher to the fact that problem based learning
would be more effective than structured exercises.
Table 1
Age
Count of
Age
1 6
2 3
3 3
Grand Total 12
Table 2
Gender Frequency
1 5
2 5
3 2
Grand Total 12
Table 3
Row Labels Frequency
1 6
2 4
3 2
Grand Total 12

5PYTHAGORAS THEOREM AND BASEBALL FIELD
Table 4
Row Labels Frequency
1 5
2 2
3 5
Grand Total 12
Table 5
Row Labels Frequency
1 6
2 4
3 2
Grand Total 12
Table 6
Row Labels Frequency
1 2
2 3
3 4
4 1
5 2
Grand Total 12
Table 7
Row Labels Frequency
1 4
2 2
4 2
5 4
Grand Total 12
Table 8
Row Labels Frequency
1 1

6PYTHAGORAS THEOREM AND BASEBALL FIELD
2 2
3 3
4 3
5 3
Grand Total 12
Conclusion
Thus, from the above discussions it can be seen that most of the people think that
structured exercises are better than activity based learning. Solving exercises makes them
more clear about the topic. Application of the topics and activities will only be performed by
the students only after they have a clear understanding of the subject.