OOT2 GLM2
TASK 3 – Passed
History in Mathematics GLM2
Western Governors University
, 1 April 2025
History in Mathematics GLM2- Task 3
A. Discuss one of the following discrete mathematics topics and its historical
development over time. Include contributions from two significant individuals,
entities, or cultures:
Sequences and series have played a crucial role in the development of
mathematics, with their study tracing back to ancient civilizations. The earliest
recorded exploration of sequences can be found in the work of the Babylonians,
who were familiar with numerical patterns related to multiplication and division.
However, it was the ancient Greeks, particularly Euclid, who made significant
strides in formalizing the understanding of numbers and sequences. Euclid's work
in geometry, especially in his "Elements," contained principles that later influenced
the understanding of numerical sequences. The Greeks also developed early forms
of arithmetic progressions and began to analyze sums of series, laying the
groundwork for more advanced theories.
One of the most significant contributions to the study of sequences and series
came from the Indian mathematician Aryabhata (476–550 CE). Aryabhata
developed advanced methods for summing series and sequences, particularly in
trigonometry, and his work influenced later developments in calculus. His
exploration of the sine function, along with the use of series expansions,
contributed to the formalization of trigonometric series. Additionally, the works of
European mathematicians during the Renaissance, such as Fibonacci, brought the
study of sequences into focus with his famous Fibonacci sequence. This sequence
has since been applied in numerous fields, including biology, computer science, and
finance. These contributions set the stage for the rigorous study of infinite series,
culminating in the work of Isaac Newton and Gottfried Wilhelm Leibniz during the
17th century, who formalized the concept of calculus, including the study of
convergent series.
B. Discuss the creation of one of the following units of measurement and its historical
development over time:
The concept of radians as a measure of angles developed over time through the
contributions of various mathematicians. The idea of using the radius of a circle to
measure angles can be traced back to ancient Greek mathematicians, who explored
the relationships between angles, arcs, and circles. Early systems of angle
measurement, such as degrees, divided a circle into 360 parts based on astronomical
observations, which originated with Babylonian astronomers. However, the clear
notion of using the radius as a fundamental unit of angular measure did not emerge
until the 17th century. The formal introduction of radians came from the French
mathematician Roger Cotes in the early 1700s. Cotes recognized that a more natural
and algebraically convenient way to measure angles involved the length of the arc
subtended by the angle, which is proportional to the radius of the circle.
The widespread adoption of the radian system began when Leonhard Euler (1707–
1783) incorporated it into his work on trigonometry and calculus. Euler’s
contributions, particularly his development of Euler’s formula for complex numbers,
played a crucial role in establishing radians as the standard unit for angular
measurement in mathematical analysis. Throughout the 18th and 19th centuries, as
calculus became increasingly central to mathematics and science, the use of radians
proved essential for simplifying many formulas, especially in calculus and physics,
where angular velocities and other trigonometric applications are frequently
This study source was downloaded by 100000901969919 from CourseHero.com on 11-01-2025 18:15:38 GMT -05:00
https://www.coursehero.com/file/251822460/OOT2-GLM2-Task-3docx/
TASK 3 – Passed
History in Mathematics GLM2
Western Governors University
, 1 April 2025
History in Mathematics GLM2- Task 3
A. Discuss one of the following discrete mathematics topics and its historical
development over time. Include contributions from two significant individuals,
entities, or cultures:
Sequences and series have played a crucial role in the development of
mathematics, with their study tracing back to ancient civilizations. The earliest
recorded exploration of sequences can be found in the work of the Babylonians,
who were familiar with numerical patterns related to multiplication and division.
However, it was the ancient Greeks, particularly Euclid, who made significant
strides in formalizing the understanding of numbers and sequences. Euclid's work
in geometry, especially in his "Elements," contained principles that later influenced
the understanding of numerical sequences. The Greeks also developed early forms
of arithmetic progressions and began to analyze sums of series, laying the
groundwork for more advanced theories.
One of the most significant contributions to the study of sequences and series
came from the Indian mathematician Aryabhata (476–550 CE). Aryabhata
developed advanced methods for summing series and sequences, particularly in
trigonometry, and his work influenced later developments in calculus. His
exploration of the sine function, along with the use of series expansions,
contributed to the formalization of trigonometric series. Additionally, the works of
European mathematicians during the Renaissance, such as Fibonacci, brought the
study of sequences into focus with his famous Fibonacci sequence. This sequence
has since been applied in numerous fields, including biology, computer science, and
finance. These contributions set the stage for the rigorous study of infinite series,
culminating in the work of Isaac Newton and Gottfried Wilhelm Leibniz during the
17th century, who formalized the concept of calculus, including the study of
convergent series.
B. Discuss the creation of one of the following units of measurement and its historical
development over time:
The concept of radians as a measure of angles developed over time through the
contributions of various mathematicians. The idea of using the radius of a circle to
measure angles can be traced back to ancient Greek mathematicians, who explored
the relationships between angles, arcs, and circles. Early systems of angle
measurement, such as degrees, divided a circle into 360 parts based on astronomical
observations, which originated with Babylonian astronomers. However, the clear
notion of using the radius as a fundamental unit of angular measure did not emerge
until the 17th century. The formal introduction of radians came from the French
mathematician Roger Cotes in the early 1700s. Cotes recognized that a more natural
and algebraically convenient way to measure angles involved the length of the arc
subtended by the angle, which is proportional to the radius of the circle.
The widespread adoption of the radian system began when Leonhard Euler (1707–
1783) incorporated it into his work on trigonometry and calculus. Euler’s
contributions, particularly his development of Euler’s formula for complex numbers,
played a crucial role in establishing radians as the standard unit for angular
measurement in mathematical analysis. Throughout the 18th and 19th centuries, as
calculus became increasingly central to mathematics and science, the use of radians
proved essential for simplifying many formulas, especially in calculus and physics,
where angular velocities and other trigonometric applications are frequently
This study source was downloaded by 100000901969919 from CourseHero.com on 11-01-2025 18:15:38 GMT -05:00
https://www.coursehero.com/file/251822460/OOT2-GLM2-Task-3docx/
