ACI2605
Assignment 3
Unique No: 89110
Due 3 July 2025
, Assignment 3
Question 1: The History of Numbers
Steen (1988:611-6) defines mathematics as “the science of patterns” and explains that
mathematicians seek and analyze patterns in various fields. He notes that mathematical
theories help explain relationships between patterns and that these patterns can be
applied to real world phenomena.
1.1 Provide a critical analysis of Steen’s (1988) definition of mathematics in
relation to:
1.1.1 The Binary Number System
Steen’s perspective that mathematics is the study of patterns is clearly applicable to the
binary number system, which uses only two digits: 0 and 1. These two digits form the
foundational pattern for digital computing and information processing.
• Pattern Recognition: Binary numbers follow predictable, repeating patterns based
on powers of 2 (e.g., 1, 10, 11, 100…). These patterns are consistent and can be
extended infinitely.
• Mathematical Structures: As Steen mentions, mathematics builds structures from
patterns. The binary system supports structures like Boolean algebra and logic
circuits, where patterns of 1s and 0s determine system outputs.
• Application in Technology: The binary number system exemplifies how
mathematical patterns are used in practical applications, such as data storage,
image processing, and machine learning. Every piece of digital data is stored in
binary demonstrating the predictive and explanatory power Steen refers to.
• Functions and Operators: In binary, operations such as addition, multiplication, or
logical gates (AND, OR, NOT) demonstrate how operators bind binary patterns to
produce results another alignment with Steen’s definition.
Critical Insight:
The binary system validates Steen’s view that mathematics is the study of patterns. It
Assignment 3
Unique No: 89110
Due 3 July 2025
, Assignment 3
Question 1: The History of Numbers
Steen (1988:611-6) defines mathematics as “the science of patterns” and explains that
mathematicians seek and analyze patterns in various fields. He notes that mathematical
theories help explain relationships between patterns and that these patterns can be
applied to real world phenomena.
1.1 Provide a critical analysis of Steen’s (1988) definition of mathematics in
relation to:
1.1.1 The Binary Number System
Steen’s perspective that mathematics is the study of patterns is clearly applicable to the
binary number system, which uses only two digits: 0 and 1. These two digits form the
foundational pattern for digital computing and information processing.
• Pattern Recognition: Binary numbers follow predictable, repeating patterns based
on powers of 2 (e.g., 1, 10, 11, 100…). These patterns are consistent and can be
extended infinitely.
• Mathematical Structures: As Steen mentions, mathematics builds structures from
patterns. The binary system supports structures like Boolean algebra and logic
circuits, where patterns of 1s and 0s determine system outputs.
• Application in Technology: The binary number system exemplifies how
mathematical patterns are used in practical applications, such as data storage,
image processing, and machine learning. Every piece of digital data is stored in
binary demonstrating the predictive and explanatory power Steen refers to.
• Functions and Operators: In binary, operations such as addition, multiplication, or
logical gates (AND, OR, NOT) demonstrate how operators bind binary patterns to
produce results another alignment with Steen’s definition.
Critical Insight:
The binary system validates Steen’s view that mathematics is the study of patterns. It
