BEAUTY OF MATHS
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This short document discusses checking the beauty of mathematics and was prepared by Vijithra Gopal.J. It does not provide any details about mathematics or what will be checked.
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Branches of mathematics
Mathematics can be divided into various branches based on different classification schemes. A traditional division is into pure mathematics, which is studied for its own interest, and applied mathematics, which can be directly applied to real world problems. Some key branches include:
Arithmetic, the oldest branch involving the study of numbers and basic operations between them.
Algebra, which studies the properties of numbers and methods to solve equations, leading to abstract algebra and concepts like vectors.
Mathematical analysis, concerning continuous change and theories like differentiation, integration and limits.
Combinatorics, focused on discrete collections and their structures, including graph theory and counting objects.
Geometry and topology, dealing with spatial relationships using axioms
Branches of mathematics
Mathematics can be divided into several branches that each focus on different areas of study. Some of the main branches include arithmetic, algebra, mathematical analysis, combinatorics, and geometry/topology. Arithmetic is the oldest branch and focuses on numbers and basic operations like addition and multiplication. Algebra studies the properties of numbers and methods for solving equations. Mathematical analysis examines continuous change through calculus, limits, and functions. Combinatorics analyzes discrete collections of objects and their relationships. Geometry and topology use spatial relationships and properties of shapes.
Patterns
Mathematical patterns come in many forms. Some patterns repeat, some grow, and others shrink or change in predictable ways. Understanding patterns helps make sense of numbers and relationships in the real world.
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The Seven Bridges of Königsberg is a historically notable math problem where the city of Königsberg, Prussia (now Kaliningrad, Russia) was divided by a river and included two islands connected to the mainland and each other by seven bridges. Leonhard Euler proved in 1736 that there was no possible walk through the city where a person could cross each bridge once and only once, laying the foundations for graph theory and topology.
TrigNOMETRY
Early study of trigonometry began with the ancient Egyptians and Babylonians studying properties of triangles in the 2nd millennium BC. This study continued and advanced in Hellenistic Greece and India, where systematic study of trigonometric functions began. During the Middle Ages, Islamic mathematicians adopted trigonometry as a separate subject and it spread to Western Europe in the Renaissance. Modern trigonometry developed further during the 17th-18th centuries with key contributions from mathematicians like Newton, Stirling, and Euler.
TriANGLES
A triangle is a three-sided polygon with three vertices and edges, it is one of the basic shapes in geometry. Any three non-collinear points determine a unique triangle that exists on a single two-dimensional plane. Triangles can be categorized into different types defined by their side lengths or angles.
Ramanujan number
1729 is known as the Hardy–Ramanujan number because of a famous anecdote involving the mathematicians G. H. Hardy and Srinivasa Ramanujan. When Hardy remarked that the taxi cab number 1729 seemed dull, Ramanujan revealed that 1729 can be expressed as the sum of two cubes in two different ways: 1729 = 13 + 123 = 93 + 103. This makes 1729 the smallest number that can be expressed in two distinct ways as the sum of cubes, earning it the description of a "taxicab number."
Mathematics in daily life
Mathematics is an essential skill used in many aspects of daily life. Cooking requires measuring ingredients accurately which may involve multiplication or division. Managing personal finances at the bank requires an understanding of basic math concepts to avoid financial problems. Keeping schedules and diaries for appointments relies on an ability to track times and dates mathematically. Statistics drawn from history are also important for understanding what has worked and not worked in the past to bring balance and structure going forward. Overall, modern life involves using numbers and basic math concepts in activities like cell phone use, cooking, banking, record keeping, and scheduling.
Recommended
Branches of mathematics
Mathematics can be divided into various branches based on different classification schemes. A traditional division is into pure mathematics, which is studied for its own interest, and applied mathematics, which can be directly applied to real world problems. Some key branches include:
Arithmetic, the oldest branch involving the study of numbers and basic operations between them.
Algebra, which studies the properties of numbers and methods to solve equations, leading to abstract algebra and concepts like vectors.
Mathematical analysis, concerning continuous change and theories like differentiation, integration and limits.
Combinatorics, focused on discrete collections and their structures, including graph theory and counting objects.
Geometry and topology, dealing with spatial relationships using axioms
Branches of mathematics
Mathematics can be divided into several branches that each focus on different areas of study. Some of the main branches include arithmetic, algebra, mathematical analysis, combinatorics, and geometry/topology. Arithmetic is the oldest branch and focuses on numbers and basic operations like addition and multiplication. Algebra studies the properties of numbers and methods for solving equations. Mathematical analysis examines continuous change through calculus, limits, and functions. Combinatorics analyzes discrete collections of objects and their relationships. Geometry and topology use spatial relationships and properties of shapes.
Patterns
Mathematical patterns come in many forms. Some patterns repeat, some grow, and others shrink or change in predictable ways. Understanding patterns helps make sense of numbers and relationships in the real world.
Presentation1
The Seven Bridges of Königsberg is a historically notable math problem where the city of Königsberg, Prussia (now Kaliningrad, Russia) was divided by a river and included two islands connected to the mainland and each other by seven bridges. Leonhard Euler proved in 1736 that there was no possible walk through the city where a person could cross each bridge once and only once, laying the foundations for graph theory and topology.
TrigNOMETRY
Early study of trigonometry began with the ancient Egyptians and Babylonians studying properties of triangles in the 2nd millennium BC. This study continued and advanced in Hellenistic Greece and India, where systematic study of trigonometric functions began. During the Middle Ages, Islamic mathematicians adopted trigonometry as a separate subject and it spread to Western Europe in the Renaissance. Modern trigonometry developed further during the 17th-18th centuries with key contributions from mathematicians like Newton, Stirling, and Euler.
TriANGLES
A triangle is a three-sided polygon with three vertices and edges, it is one of the basic shapes in geometry. Any three non-collinear points determine a unique triangle that exists on a single two-dimensional plane. Triangles can be categorized into different types defined by their side lengths or angles.
Ramanujan number
1729 is known as the Hardy–Ramanujan number because of a famous anecdote involving the mathematicians G. H. Hardy and Srinivasa Ramanujan. When Hardy remarked that the taxi cab number 1729 seemed dull, Ramanujan revealed that 1729 can be expressed as the sum of two cubes in two different ways: 1729 = 13 + 123 = 93 + 103. This makes 1729 the smallest number that can be expressed in two distinct ways as the sum of cubes, earning it the description of a "taxicab number."
Mathematics in daily life
Mathematics is an essential skill used in many aspects of daily life. Cooking requires measuring ingredients accurately which may involve multiplication or division. Managing personal finances at the bank requires an understanding of basic math concepts to avoid financial problems. Keeping schedules and diaries for appointments relies on an ability to track times and dates mathematically. Statistics drawn from history are also important for understanding what has worked and not worked in the past to bring balance and structure going forward. Overall, modern life involves using numbers and basic math concepts in activities like cell phone use, cooking, banking, record keeping, and scheduling.
Correlation
Mathematics is applied in various branches of science:
- In physics, mathematics is an essential tool and physics inspires new mathematics.
- In chemistry, mathematical modeling is used to model chemical phenomena.
- In biology, precise mathematical models are needed to represent complex biological systems like protein interactions, and quantitative modeling allows simulation and prediction of properties.
- In social sciences, mathematics is used to model fields like economics, psychology, and political science through techniques like game theory and decision modeling.
Ancient mathematicians
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Ancient mathematicians
This document discusses the importance of education in empowering women. It states that educating girls and women enables them to make their own decisions, stand up against discrimination, and access jobs that help them gain financial independence. With education, women can become advocates for gender equality and play a greater role in transforming society.
Vedic
Vedic mathematics is a technique for calculation based on 16 sutras or aphorisms rediscovered from ancient Vedic texts between 1911-1918. It was developed by Sri Bharati Krishna Tirthaji Maharaj and allows users to mentally solve even difficult mathematical problems quickly through memorization of the sutras and their corollaries. The methods are described as coherent, flexible, mental, memory-improving, appealing to all people, and increasing mental agility while being efficient, fast, easy, and fun.
Ramanujan
Srinivasa Ramanujan was a self-taught Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. He impressed his teachers as a student with his natural talent and intuition for mathematics. Although hindered by poverty and ill health, his work enriched fields like number theory and later inspired physics. Ramanujan's letters and notebooks were filled with thousands of theorems and identities he had discovered on his own.
Pascal's triangle
Pascal's triangle is a number pattern where each number is the sum of the two numbers directly above it. The pattern is created by adding numbers above to generate the numbers below, such as 1 + 3 = 4 as highlighted in the example. Pascal's triangle demonstrates an interesting way that numbers can be combined in a triangular formation according to specific rules.
Mathematical puzzles
Mathematical puzzles are an important part of recreational mathematics. They have set rules like video games but usually do not involve competition. To solve them, one must find a solution that satisfies the given conditions using mathematical logic. Common types are logic puzzles which require mathematical thinking to solve.
Geometry
Geometry is a branch of mathematics focused on shapes, their size, position, and properties of space. Two-dimensional shapes like squares and circles only have length and width without thickness, while three-dimensional objects have height, width, and depth like real-world bodies.
Quotes about mathematicians
This document contains 11 quotes from famous mathematicians and thinkers about mathematics. Some of the quotes discuss mathematics as being uncertain when applied to reality, as a tool used by God, and as something that causes both minor problems and greater problems for Einstein. The quotes cover a range of perspectives on mathematics from several influential individuals.
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A mathematician is someone with extensive knowledge of mathematics who uses it to solve mathematical problems. Mathematics is concerned with quantities like numbers, data, structures, spaces, models and change. Some famous mathematicians include Sir Isaac Newton, Archimedes, Fibonacci, and Omar Khayyam.
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Mathematics is defined as the study of quantity, structure, space, and change. It involves patterns, formulas, and relationships. The main branches of mathematics include arithmetic, algebra, geometry, calculus, and statistics.
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- In chemistry, mathematical modeling is used to model chemical phenomena.
- In biology, precise mathematical models are needed to represent complex biological systems like protein interactions, and quantitative modeling allows simulation and prediction of properties.
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