Answer :
Answer:
Maths Journal: Exploring Mathematics through Art
Article a) Evolution of the Number System from Natural Numbers to Real Numbers
The evolution of number systems spans centuries and cultures, evolving from the simplest natural numbers to the complex real numbers we use today. Begin with:
Natural Numbers: Used for counting (1, 2, 3, ...).
Whole Numbers: Include zero (0, 1, 2, 3, ...).
Integers: Include negative numbers (... -3, -2, -1, 0, 1, 2, 3, ...).
Rational Numbers: Fractions and decimals that can be expressed as a ratio of integers.
Irrational Numbers: Numbers that cannot be expressed as a fraction (π, √2).
Real Numbers: Include all rational and irrational numbers.
Support your explanations with artistic representations of each number type, perhaps using symbols or visual representations (like number lines).
Article b) Use your imagination and art skills to draw pictures to support your write-up of this journal.
Create visual representations for each stage of the number system evolution. For example:
Natural numbers: Draw a series of objects (stars, apples) representing counts.
Integers: Represent positive and negative numbers on a number line.
Rational and irrational numbers: Visualize fractions and irrational constants like π using geometric shapes or artistic interpretations.
Article c) Will the journey continue further after the real number system? What do you think- support with explanation and examples?
Discuss the possibility of extending beyond real numbers:
Complex Numbers: Include a real part and an imaginary part (a + bi, where i is the imaginary unit √(-1)).
Hyperreal Numbers: Infinitesimally small and large numbers used in non-standard analysis.
Quaternions and beyond: Algebraic structures extending beyond complex numbers.
Explain with examples from physics (quantum mechanics, relativity) and mathematics (complex analysis, higher dimensions).
Article d) Properties of real numbers
Detail essential properties of real numbers:
Closure: Sum and product of two real numbers are real.
Commutativity: Order doesn't affect addition and multiplication.
Associativity: Grouping doesn't affect addition and multiplication.
Distributivity: Multiplication distributes over addition.
Identity and Inverses: Existence of additive and multiplicative identities and inverses.
Accompany with visual aids illustrating these properties through diagrams or equations.
Article e) Real Life Problems
Apply real numbers to practical problems:
Finance: Compound interest calculations.
Physics: Calculating distances, forces, and energy.
Engineering: Designing structures using mathematical models.
Statistics: Analyzing data sets.
Include artistic representations of real-world scenarios where real number calculations are crucial.