India’s contribution to geometry[1]
•Download as PPT, PDF•
0 likes•1,016 views
This document summarizes a presentation given in India on the construction of an isosceles trapezium. It defines a trapezium as a quadrilateral with one set of parallel sides. An isosceles trapezium is then defined as a trapezium with congruent legs and base angles. The document discusses the Indian mathematician Baudhāyana and his contributions to geometry in the 800s BCE, including calculating pi and discovering the Pythagorean theorem. It then demonstrates how to construct an isosceles trapezium by drawing two parallel lines, finding the midpoint, and using a compass to draw arcs intersecting the parallel lines.
Report
Share
Report
Share
Recommended
Circles and coordinate circles
terms on circles, tangent lines, secant lines, area & perimeter, sector of a circle. equation of a circle.
Greek mathematics
This document summarizes the contributions of several important ancient Greek mathematicians including Pythagoras who discovered proportion, geometry, number theory and proof; Aristotle who taught Alexander the Great subjects like medicine, philosophy, math, morals and logic; Euclid who wrote the influential Elements textbook still used today; Archimedes who made discoveries in volume and buoyancy; and Eratosthenes who calculated the circumference of the Earth and invented the leap year calendar.
quadraticequations-111211090004-phpapp02 (2).pdf
Quadratic equations take the form of ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0. There are three main ways to solve quadratic equations: factoring, completing the square, and using the quadratic formula. Factoring involves finding two linear expressions whose product is the quadratic expression. Completing the square transforms the equation into the form (x + p)^2 = q. The quadratic formula provides exact solutions for x in terms of a, b, and c. The discriminant, b^2 - 4ac, determines the nature of the roots.
Solving Inequalities (Algebra 2)
The document discusses various methods for solving inequalities, including:
- Properties for adding, subtracting, multiplying, and dividing terms within an inequality
- Using set-builder and interval notation to describe the solution set of an inequality
- Graphical representations using open and closed circles to indicate whether a number is or isn't part of the solution set
The document provides examples of applying these different techniques to solve specific inequalities.
Lesson plan - angle sum of triangle
This lesson plan introduces students to the angle sum of a triangle through three methods: measuring angles with protractors, cutting out triangles and rearranging the corners, and using GeoGebra software. Students will work in groups to measure angles, cut out triangles, and explore interactive worksheets. They will discover that regardless of the type of triangle, the interior angles always sum to 180 degrees. The lesson concludes with an assessment involving calculating unknown angles based on given measures.
Binomial theorem
The Binomial Theorem provides a formula for expanding binomial expressions of the form (a + b)^n. It states that the terms follow a predictable pattern based on exponents of the variables a and b and coefficients determined by Pascal's Triangle. The theorem was first discovered by Isaac Newton and can be written as a general formula involving factorials and binomial coefficients. It allows for the easy expansion of binomials without having to manually multiply out each term.
4.1 inverse functions t
This document provides examples and exercises on inverse functions. It first shows an example of finding the inverse of the function f(x) = 2x-3/(x+2). It gives the steps to solve for x in terms of y and obtain the inverse function f^-1(x) = -2x-3/(x-2). It then asks the reader to verify that f(f^-1(x)) = x. The exercises provide 20 functions and ask the reader to find their inverses and verify the inverses are correct. It also gives graphs of 8 functions and asks the reader to determine properties of the inverse graphs, including their domains and ranges and any fixed or end points.
Recommended
Circles and coordinate circles
terms on circles, tangent lines, secant lines, area & perimeter, sector of a circle. equation of a circle.
Greek mathematics
This document summarizes the contributions of several important ancient Greek mathematicians including Pythagoras who discovered proportion, geometry, number theory and proof; Aristotle who taught Alexander the Great subjects like medicine, philosophy, math, morals and logic; Euclid who wrote the influential Elements textbook still used today; Archimedes who made discoveries in volume and buoyancy; and Eratosthenes who calculated the circumference of the Earth and invented the leap year calendar.
quadraticequations-111211090004-phpapp02 (2).pdf
Quadratic equations take the form of ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0. There are three main ways to solve quadratic equations: factoring, completing the square, and using the quadratic formula. Factoring involves finding two linear expressions whose product is the quadratic expression. Completing the square transforms the equation into the form (x + p)^2 = q. The quadratic formula provides exact solutions for x in terms of a, b, and c. The discriminant, b^2 - 4ac, determines the nature of the roots.
Solving Inequalities (Algebra 2)
The document discusses various methods for solving inequalities, including:
- Properties for adding, subtracting, multiplying, and dividing terms within an inequality
- Using set-builder and interval notation to describe the solution set of an inequality
- Graphical representations using open and closed circles to indicate whether a number is or isn't part of the solution set
The document provides examples of applying these different techniques to solve specific inequalities.
Lesson plan - angle sum of triangle
This lesson plan introduces students to the angle sum of a triangle through three methods: measuring angles with protractors, cutting out triangles and rearranging the corners, and using GeoGebra software. Students will work in groups to measure angles, cut out triangles, and explore interactive worksheets. They will discover that regardless of the type of triangle, the interior angles always sum to 180 degrees. The lesson concludes with an assessment involving calculating unknown angles based on given measures.
Binomial theorem
The Binomial Theorem provides a formula for expanding binomial expressions of the form (a + b)^n. It states that the terms follow a predictable pattern based on exponents of the variables a and b and coefficients determined by Pascal's Triangle. The theorem was first discovered by Isaac Newton and can be written as a general formula involving factorials and binomial coefficients. It allows for the easy expansion of binomials without having to manually multiply out each term.
4.1 inverse functions t
This document provides examples and exercises on inverse functions. It first shows an example of finding the inverse of the function f(x) = 2x-3/(x+2). It gives the steps to solve for x in terms of y and obtain the inverse function f^-1(x) = -2x-3/(x-2). It then asks the reader to verify that f(f^-1(x)) = x. The exercises provide 20 functions and ask the reader to find their inverses and verify the inverses are correct. It also gives graphs of 8 functions and asks the reader to determine properties of the inverse graphs, including their domains and ranges and any fixed or end points.
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
- A trapezoid is a quadrilateral with one pair of parallel sides called the bases. The non-parallel sides are called the legs.
- An isosceles trapezoid has one pair of parallel sides and one pair of congruent non-parallel sides called legs.
- Theorems about the isosceles trapezoid include: the base angles are congruent, opposite angles are supplementary, and the diagonals are congruent.
- The median of any trapezoid is parallel to the bases and is equal to half the sum of the bases.
Final india’s contribution to geometry[1]
The Shulba Sutras are ancient Indian texts containing geometrical constructions and are considered the earliest sources on Indian mathematics. Four major Shulba Sutras were composed between 800 BCE to 200 CE, with the oldest attributed to Baudhayana around 800 BCE. The Baudhayana Shulba Sutra contains geometric constructions of shapes like squares and rectangles as well as area-preserving transformations. It provides what is considered one of the earliest statements of the Pythagorean theorem and an approximation of pi. The text also describes how to dissect a rectangle into three pieces that can be rearranged to form a square.
geometricalconstruction-101112193228-phpapp01.pptx
This document provides instructions for performing various geometric constructions. It begins with introductory information on points, lines, and common geometric shapes. It then provides step-by-step instructions for constructing angles, triangles, circles, quadrilaterals, regular polygons, tangents to circles, joining circles, ellipses, involutes, and more. The constructions require only a compass and straightedge. Accuracy is emphasized as the key difficulty.
Maths sa 2 synopsis
The document provides information about topics in grade 9 math, including:
1) Linear equations in two variables and their graphical representations as lines.
2) Properties of quadrilaterals such as parallelograms, and how to classify them.
3) Finding areas of parallelograms, triangles, and how these shapes are related.
4) Properties of circles such as angles subtended by chords and arcs.
Geometricalconstruction
This document provides instructions for performing various geometric constructions. It begins with an introduction on the importance of geometric constructions in engineering drawing. It then covers techniques for constructing lines, angles, triangles, circles, quadrilaterals, regular polygons, tangents to circles, joining circles, ellipses, and involutes. The document provides detailed step-by-step instructions for over 30 different geometric constructions, with diagrams to illustrate each method. Accuracy is emphasized as the main difficulty in geometric constructions.
Class 5 presentation
The document provides information for an engineering class including the instructor's name and class details, assignments due dates and details, and content on surveying techniques and geometric constructions. Key points covered include potential errors in surveying, definitions of surveying, examples of historical errors, instructions for groups to practice drawing techniques, and methods for drawing various geometric shapes and their intersections.
Triangles and its all types
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Triangles X CLASS CBSE NCERT
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of similar triangles, including the AAA, SSS, SAS, and AA similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles discussed include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Triangles
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
TRIANGLE CONGRUENCE, SSS, ASA, SAS and AAS
This document discusses congruent triangles and their properties. It begins by introducing triangles and their historical uses. It then defines different types of triangles based on their sides and angles. The document explains the triangle congruence postulates of SSS, SAS, ASA, and uses examples to prove triangles congruent. It also discusses using congruent triangles to solve real-world problems involving structures. The document warns that there is no SSA or AAA postulate for triangle congruence. It concludes by discussing properties of isosceles and equilateral triangles.
Mathematician marathi
Aryabhata was an Indian mathematician and astronomer born in 476 CE in Patna, India who made early contributions to trigonometry and developed concepts of sine, cosine, and versine. Some of his key
C1 g9-s1-t7-2
The document summarizes key concepts from Grade 9 math chapters on linear equations in two variables, quadrilaterals, areas of parallelograms and triangles, circles, constructions, and surface areas and volumes. It defines linear equations in two variables and their graphical representations as lines. It also describes properties and classifications of quadrilaterals, parallelograms, and triangles. Additionally, it covers circle concepts like congruent circles, angles subtended by chords, and concyclic points. Construction methods for triangles are provided when certain parts are given. Finally, formulas for surface areas and volumes of cubes, cuboids, cylinders, cones, and spheres are stated.
Mensuration,direct and indirect speech,
This document discusses various topics in mensuration including the formulas for calculating the area and perimeter of basic shapes like rectangles, parallelograms, trapezoids, triangles, cubes, cuboids, and cylinders. It also covers the concepts of direct and inverse proportion and provides examples. Finally, it discusses the construction of a quadrilateral given specific length measurements of its sides.
Basic construction
This document discusses various techniques for technical drawing, including:
- Drawing parallel and perpendicular lines
- Bisecting lines and angles
- Dividing lines into multiple sections
- Finding the center of arcs and inscribing/circumscribing circles in triangles
- Constructing regular polygons like hexagons
- Drawing ellipses, cycloids, epicycloids, and involutes
- Examples of involutes for circles and triangles are provided
- The Archimedean spiral is defined by its polar equation
Ankit1
- A triangle is a three-sided polygon with three vertices and three line segment sides.
- The area of a triangle is calculated as one half of the base multiplied by the height.
- A parallelogram is a quadrilateral with two pairs of parallel sides, and opposite angles and sides of equal measure. The area of a parallelogram is calculated as the base multiplied by the height.
- Congruent figures have the same shape and size, with corresponding parts coinciding. Figures with equal areas are not necessarily congruent.
Maths straight lines presentation
This document presents information about straight lines. It begins with an introduction to straight lines, defining them as lines with no curves that extend infinitely in both directions. It then discusses the Cartesian coordinate system and how points on a plane are located using x and y coordinates. Various applications of straight lines in areas like roads, physics, and data analysis are provided. Key concepts covered include properties of straight lines, parallel lines, and the relationship between slope and the angle of a line.
Analytical geometry
Okay, here are the steps to solve this problem:
1) The sphere has a radius of 8 inches
2) To find the volume of a sphere we use the formula: V = (4/3)πr^3
3) Plugging in the values:
V = (4/3)π(8)^3
V = (4/3)π(512)
V = 1024π
So the volume of the spherical fish tank with a radius of 8 inches is 1024π cubic inches.
contribution of mathematicians.pdf
1) Aryabhata was a 5th century Indian mathematician who made several important contributions including developing a place-value decimal system, computing π to four decimal places, and formulating algebraic formulae.
2) Carl Friedrich Gauss was an influential 19th century German mathematician and scientist who made seminal contributions across many areas of mathematics and science, including constructing a 17-sided polygon, developing complex numbers, discovering the Gaussian distribution, and conducting pioneering work in geometry, algebra, statistics, and astronomy.
3) Both Aryabhata and Gauss were pioneering mathematicians who made enduring contributions that expanded the boundaries of mathematics and influenced many subsequent scientists and mathematicians.
Golden spiral sublime
This presentation discusses the construction of the golden spiral from the sublime triangle. It begins by introducing the sublime triangle, which is made up of sides from a regular pentagon. It then demonstrates how to construct the golden spiral by repeatedly drawing angle bisectors to generate similar, smaller triangles and using the points to lay out concentric arcs that form the spiral shape. The presentation provides step-by-step instructions on drawing the angle bisectors, finding the points, and using the points and radii to construct the golden spiral arcs.
Euclids geometry
Euclid's Geometry is considered one of the most influential textbooks of all time. It introduced the axiomatic method and is the earliest example of the format still used in mathematics today. The document provides background on Euclid and the key aspects of his influential work Elements, including:
- Euclid organized geometry into a deductive system based on definitions, common notions, postulates, and propositions/theorems proved from these foundations.
- The Elements covers 13 books on topics like plane geometry, number theory, and solid geometry, containing over 450 theorems deduced from the initial assumptions.
- It established geometry as a logical science and had a major impact on mathematics and science for over 2000
Diabetes
There are four main types of diabetes: type 1, type 2, gestational diabetes, and prediabetes. Type 1 is an autoimmune disease where the body attacks the pancreas, type 2 is caused by the body not producing enough insulin or cells not responding to insulin properly. Gestational diabetes occurs during pregnancy. Prediabetes means blood sugar levels are higher than normal but not high enough to be classified as diabetes. Complications of diabetes include cardiovascular, kidney, nerve and eye diseases. Diabetes is tested through A1C, fasting plasma glucose, and oral glucose tolerance tests. Treatment options include oral medications, insulin injections, surgery, and lifestyle changes like diet and exercise. Future treatments may include gene therapy for type 1
Polynomials
This document provides an overview of polynomials, including:
- Defining polynomials as expressions involving variables and coefficients using addition, subtraction, multiplication, and exponents.
- Discussing the history of polynomial notation pioneered by Descartes.
- Explaining the different types of polynomials like monomials, binomials, and trinomials.
- Outlining common uses of polynomials in mathematics, science, and other fields.
- Describing how to find the degree of a polynomial and graph polynomial functions.
- Explaining arithmetic operations like addition, subtraction, and division that can be performed on polynomials.
More Related Content
Similar to India’s contribution to geometry[1]
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
- A trapezoid is a quadrilateral with one pair of parallel sides called the bases. The non-parallel sides are called the legs.
- An isosceles trapezoid has one pair of parallel sides and one pair of congruent non-parallel sides called legs.
- Theorems about the isosceles trapezoid include: the base angles are congruent, opposite angles are supplementary, and the diagonals are congruent.
- The median of any trapezoid is parallel to the bases and is equal to half the sum of the bases.
Final india’s contribution to geometry[1]
The Shulba Sutras are ancient Indian texts containing geometrical constructions and are considered the earliest sources on Indian mathematics. Four major Shulba Sutras were composed between 800 BCE to 200 CE, with the oldest attributed to Baudhayana around 800 BCE. The Baudhayana Shulba Sutra contains geometric constructions of shapes like squares and rectangles as well as area-preserving transformations. It provides what is considered one of the earliest statements of the Pythagorean theorem and an approximation of pi. The text also describes how to dissect a rectangle into three pieces that can be rearranged to form a square.
geometricalconstruction-101112193228-phpapp01.pptx
This document provides instructions for performing various geometric constructions. It begins with introductory information on points, lines, and common geometric shapes. It then provides step-by-step instructions for constructing angles, triangles, circles, quadrilaterals, regular polygons, tangents to circles, joining circles, ellipses, involutes, and more. The constructions require only a compass and straightedge. Accuracy is emphasized as the key difficulty.
Maths sa 2 synopsis
The document provides information about topics in grade 9 math, including:
1) Linear equations in two variables and their graphical representations as lines.
2) Properties of quadrilaterals such as parallelograms, and how to classify them.
3) Finding areas of parallelograms, triangles, and how these shapes are related.
4) Properties of circles such as angles subtended by chords and arcs.
Geometricalconstruction
This document provides instructions for performing various geometric constructions. It begins with an introduction on the importance of geometric constructions in engineering drawing. It then covers techniques for constructing lines, angles, triangles, circles, quadrilaterals, regular polygons, tangents to circles, joining circles, ellipses, and involutes. The document provides detailed step-by-step instructions for over 30 different geometric constructions, with diagrams to illustrate each method. Accuracy is emphasized as the main difficulty in geometric constructions.
Class 5 presentation
The document provides information for an engineering class including the instructor's name and class details, assignments due dates and details, and content on surveying techniques and geometric constructions. Key points covered include potential errors in surveying, definitions of surveying, examples of historical errors, instructions for groups to practice drawing techniques, and methods for drawing various geometric shapes and their intersections.
Triangles and its all types
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Triangles X CLASS CBSE NCERT
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of similar triangles, including the AAA, SSS, SAS, and AA similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles discussed include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Triangles
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
TRIANGLE CONGRUENCE, SSS, ASA, SAS and AAS
This document discusses congruent triangles and their properties. It begins by introducing triangles and their historical uses. It then defines different types of triangles based on their sides and angles. The document explains the triangle congruence postulates of SSS, SAS, ASA, and uses examples to prove triangles congruent. It also discusses using congruent triangles to solve real-world problems involving structures. The document warns that there is no SSA or AAA postulate for triangle congruence. It concludes by discussing properties of isosceles and equilateral triangles.
Mathematician marathi
Aryabhata was an Indian mathematician and astronomer born in 476 CE in Patna, India who made early contributions to trigonometry and developed concepts of sine, cosine, and versine. Some of his key
C1 g9-s1-t7-2
The document summarizes key concepts from Grade 9 math chapters on linear equations in two variables, quadrilaterals, areas of parallelograms and triangles, circles, constructions, and surface areas and volumes. It defines linear equations in two variables and their graphical representations as lines. It also describes properties and classifications of quadrilaterals, parallelograms, and triangles. Additionally, it covers circle concepts like congruent circles, angles subtended by chords, and concyclic points. Construction methods for triangles are provided when certain parts are given. Finally, formulas for surface areas and volumes of cubes, cuboids, cylinders, cones, and spheres are stated.
Mensuration,direct and indirect speech,
This document discusses various topics in mensuration including the formulas for calculating the area and perimeter of basic shapes like rectangles, parallelograms, trapezoids, triangles, cubes, cuboids, and cylinders. It also covers the concepts of direct and inverse proportion and provides examples. Finally, it discusses the construction of a quadrilateral given specific length measurements of its sides.
Basic construction
This document discusses various techniques for technical drawing, including:
- Drawing parallel and perpendicular lines
- Bisecting lines and angles
- Dividing lines into multiple sections
- Finding the center of arcs and inscribing/circumscribing circles in triangles
- Constructing regular polygons like hexagons
- Drawing ellipses, cycloids, epicycloids, and involutes
- Examples of involutes for circles and triangles are provided
- The Archimedean spiral is defined by its polar equation
Ankit1
- A triangle is a three-sided polygon with three vertices and three line segment sides.
- The area of a triangle is calculated as one half of the base multiplied by the height.
- A parallelogram is a quadrilateral with two pairs of parallel sides, and opposite angles and sides of equal measure. The area of a parallelogram is calculated as the base multiplied by the height.
- Congruent figures have the same shape and size, with corresponding parts coinciding. Figures with equal areas are not necessarily congruent.
Maths straight lines presentation
This document presents information about straight lines. It begins with an introduction to straight lines, defining them as lines with no curves that extend infinitely in both directions. It then discusses the Cartesian coordinate system and how points on a plane are located using x and y coordinates. Various applications of straight lines in areas like roads, physics, and data analysis are provided. Key concepts covered include properties of straight lines, parallel lines, and the relationship between slope and the angle of a line.
Analytical geometry
Okay, here are the steps to solve this problem:
1) The sphere has a radius of 8 inches
2) To find the volume of a sphere we use the formula: V = (4/3)πr^3
3) Plugging in the values:
V = (4/3)π(8)^3
V = (4/3)π(512)
V = 1024π
So the volume of the spherical fish tank with a radius of 8 inches is 1024π cubic inches.
contribution of mathematicians.pdf
1) Aryabhata was a 5th century Indian mathematician who made several important contributions including developing a place-value decimal system, computing π to four decimal places, and formulating algebraic formulae.
2) Carl Friedrich Gauss was an influential 19th century German mathematician and scientist who made seminal contributions across many areas of mathematics and science, including constructing a 17-sided polygon, developing complex numbers, discovering the Gaussian distribution, and conducting pioneering work in geometry, algebra, statistics, and astronomy.
3) Both Aryabhata and Gauss were pioneering mathematicians who made enduring contributions that expanded the boundaries of mathematics and influenced many subsequent scientists and mathematicians.
Golden spiral sublime
This presentation discusses the construction of the golden spiral from the sublime triangle. It begins by introducing the sublime triangle, which is made up of sides from a regular pentagon. It then demonstrates how to construct the golden spiral by repeatedly drawing angle bisectors to generate similar, smaller triangles and using the points to lay out concentric arcs that form the spiral shape. The presentation provides step-by-step instructions on drawing the angle bisectors, finding the points, and using the points and radii to construct the golden spiral arcs.
Euclids geometry
Euclid's Geometry is considered one of the most influential textbooks of all time. It introduced the axiomatic method and is the earliest example of the format still used in mathematics today. The document provides background on Euclid and the key aspects of his influential work Elements, including:
- Euclid organized geometry into a deductive system based on definitions, common notions, postulates, and propositions/theorems proved from these foundations.
- The Elements covers 13 books on topics like plane geometry, number theory, and solid geometry, containing over 450 theorems deduced from the initial assumptions.
- It established geometry as a logical science and had a major impact on mathematics and science for over 2000
Similar to India’s contribution to geometry[1] (20)
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
geometricalconstruction-101112193228-phpapp01.pptx
geometricalconstruction-101112193228-phpapp01.pptx
More from Poonam Singh
Diabetes
There are four main types of diabetes: type 1, type 2, gestational diabetes, and prediabetes. Type 1 is an autoimmune disease where the body attacks the pancreas, type 2 is caused by the body not producing enough insulin or cells not responding to insulin properly. Gestational diabetes occurs during pregnancy. Prediabetes means blood sugar levels are higher than normal but not high enough to be classified as diabetes. Complications of diabetes include cardiovascular, kidney, nerve and eye diseases. Diabetes is tested through A1C, fasting plasma glucose, and oral glucose tolerance tests. Treatment options include oral medications, insulin injections, surgery, and lifestyle changes like diet and exercise. Future treatments may include gene therapy for type 1
Polynomials
This document provides an overview of polynomials, including:
- Defining polynomials as expressions involving variables and coefficients using addition, subtraction, multiplication, and exponents.
- Discussing the history of polynomial notation pioneered by Descartes.
- Explaining the different types of polynomials like monomials, binomials, and trinomials.
- Outlining common uses of polynomials in mathematics, science, and other fields.
- Describing how to find the degree of a polynomial and graph polynomial functions.
- Explaining arithmetic operations like addition, subtraction, and division that can be performed on polynomials.
Advertising
Advertising is a paid, non-personal form of communication used to promote ideas, products, or services. The objectives of advertising include introducing new products to convince customers to try them, retaining existing customers, and winning back customers who have switched to competitors. Advertising provides benefits like employment opportunities and economic growth while allowing consumers to learn about and compare products. However, critics argue that advertising increases product prices and can confuse consumers with similar claims. Overall, while some criticisms exist, advertising plays an important role in modern business by facilitating communication with customers.
old age
This presentation discusses the importance of elders and issues they face. Elders share their life experiences and promote cultural values, acting as mentors. However, they often face neglect from busy children, loneliness, abuse, hopelessness, and helplessness. To help, the government launched pension programs, there are awareness days for elder abuse, and we can increase awareness, education, respite care, counseling, and celebrate grandparents. The presentation concludes by advocating for letting elders age gracefully with dignity and respect.
Chemistry
Osmosis is the movement of solvent molecules through a semi-permeable membrane from an area of higher solvent concentration to lower solvent concentration. The document defines hypertonic, isotonic, and hypotonic solutions and explains how osmosis causes cell shrinkage or swelling depending on the solution. It also provides examples of how osmosis is used in desalination, food concentration, and dairy concentration processes.
Diabetes mellitus
There are four main types of diabetes: type 1, type 2, gestational diabetes, and prediabetes. Type 1 is an autoimmune disease where the body attacks the pancreas, type 2 is caused by the body not producing enough insulin or cells not responding to insulin properly. Gestational diabetes occurs during pregnancy. Prediabetes means blood sugar levels are higher than normal but not high enough to be classified as diabetes. Complications of diabetes include cardiovascular, kidney, nerve and eye diseases. Diabetes is tested through A1C, fasting plasma glucose, and oral glucose tolerance tests. Treatment options include oral medications, insulin injections, surgery, and lifestyle changes like diet and exercise. Future treatments may include gene therapy for type 1
WATER CRISIS “Prediction of 3rd world war”
The document discusses the global water crisis and issues around water management. It notes that water scarcity is increasing due to rising populations and demands for water exceeding supply. The document also discusses historical water management practices, current issues like decreasing groundwater levels, and calls for sustainable water management through conservation efforts, innovative practices, and ensuring access to safe drinking water for all. Scientists warn that without addressing water shortages, wars may be fought over water in the future and ecosystems will suffer serious damage.
Issue of Shares
The document discusses key differences between private and public companies. It states that private companies have restrictions on the number of members and cannot invite the public to subscribe to its shares, while public companies can have an unlimited number of members and can invite public subscription. Additionally, private companies have restrictions on the transfer of shares while public companies do not.
My experience my values 7th
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Solid
The document summarizes key concepts about crystalline and amorphous solids, including:
- Crystalline solids exhibit long-range order while amorphous solids only have short-range order.
- Ionic crystals like NaCl and CsCl form face-centered cubic or body-centered cubic structures to maximize interactions between oppositely charged ions.
- The cohesive energy of ionic crystals can be calculated by considering contributions from Coulomb attraction, electron overlap repulsion, ionization energies, and electron affinities.
Smart class
This document discusses the factors that influence demand, including price, income, and the prices of substitute and complementary goods. It defines quantity demanded as a change in demand due to a change in price, while a change in demand is due to other factors. A demand schedule shows the inverse relationship between price and quantity demanded in a table. A demand curve graphs this relationship, with quantity demanded on the y-axis and price on the x-axis. Movement along the demand curve occurs when quantity demanded changes due to a change in price.
S107
Cancer immunotherapy harnesses the body's immune system to fight cancer by developing antibodies or T cells that target and destroy cancer cells. Researchers are working to develop new immunotherapy approaches that use antibodies or T cells to identify and eliminate cancer cells while leaving normal cells unharmed. Immunotherapy holds promise as a revolutionary new approach for treating many cancer types by giving the body's own immune system tools to fight the disease.
S104
Solid is a state of matter where particles are arranged closely together. Constituent particles in solids can be atoms, molecules, or ions arranged in a definite pattern with no definite shape or volume. There are different types of unit cell structures that describe the arrangement of particles in solids, including primitive, body-centered, and face-centered unit cells. Close packing of spheres in two and three dimensions results in different crystal structures depending on how additional layers are arranged in the voids between lower layers.
S103
This document summarizes different types of work, energy, and collisions. It defines positive, negative, and zero work done based on the angle between the applied force and displacement. Kinetic energy is defined as the energy of motion, while potential energy is the energy due to position. The equations for kinetic and potential energy are provided. Conservation of energy and conservative versus non-conservative forces are also summarized. Kinetic energy and total linear momentum are stated to be conserved, while inelastic collisions are defined as those where the initial and final kinetic energies are not equal.
S102
This document discusses the structure and function of neurons and the nervous system. It describes the key parts of a neuron including the cell body, dendrites, and axon. It explains how nerve impulses are transmitted across synapses using neurotransmitters. The document then provides an overview of the major structures of the brain including the cerebrum, cerebellum, brainstem, and how the brain acts as the command center to integrate sensory input and control coordination.
S101
The document provides tips for conserving electricity and reducing energy costs, such as turning off lights and appliances when not in use, using more efficient appliances like CFL bulbs and gas water heaters, avoiding unnecessary opening of refrigerators, not leaving devices on standby, doing laundry in batches, and installing solar panels. It also notes that Energy Star certified devices use 20-30% less energy.
Projectile motion
Projectile motion can be thought of as the combination of horizontal and vertical motion. The horizontal motion is unaffected by gravity and follows the equation x=u*cosθ*t, while the vertical motion is affected by gravity and follows the equation y=u*sinθ*t - 0.5*g*t^2. The path of a projectile forms a parabolic curve. Factors like the launch angle and initial velocity determine the time of flight, maximum height, and horizontal range of the projectile. Projectile motion has applications in various sports to calculate the optimal angle for maximum distance.
Mansi
Anees Jung's book Lost Spring focuses on stories of children from deprived backgrounds who face difficult circumstances like being kidnapped and forced to work in the carpet industry. Some children are maltreated by alcoholic fathers, married off early, or sexually abused. In this chapter, Jung expresses concern over the exploitation of children forced to do hazardous jobs like bangle making and rag picking due to poverty and traditions. This results in the loss of childhood, education, and opportunities. One story focuses on Mukesh, who lives with his brother doing bangle making in Firozabad but wants a different career, though people believe their fate is predetermined by their previous birth. The theme of the book and awards is to create awareness about child
Gravitation
1. The document summarizes Newton's theory of gravitation and key concepts in physics such as the four fundamental forces, Newton's law of universal gravitation, and gravitational potential energy.
2. It also discusses Einstein's theory of general relativity, which improved on Newton's theory by accounting for the fact that gravity propagates at the speed of light rather than instantaneously.
3. The principle of equivalence formed the basis for general relativity and implies that accelerated frames are equivalent to gravitational fields.
More from Poonam Singh (20)
India’s contribution to geometry[1]
- 1. INDIA’S CONTRIBUTION TO GEOMETRY AT BHIDE GIRLS’ HIGH SCHOOL, NAGPUR 1ST & 2ND DECEMBER, 2012
- 2. CONSTRUCTION OF ISOSCELES TRAPEZIUM Presented by- Rishi Agrawal, Head, Dept. of Mathematics, Hislop College, Nagpur. Tithi Agrawal, Grade – 7, Edify School, Nagpur.
- 3. TRAPEZIUM (TRAPEZOID) I have only one set of parallel sides. My median is parallel to the bases and equal to one-half the sum of the bases.
- 4. Isosceles Trapezoid I have: - only one set of parallel sides - base angles congruent - legs congruent - diagonals congruent - opposite angles supplementary ISOSCELES TRAPEZOID
- 5. ISOSCELES TRAPEZIUM IN DAILY LIFE
- 6. Baudhāyana, (fl. c. 800 BCE) was an Indian mathematician, who was most likely also a priest. He is noted as the author of the earliest Sulba Sūtra—appendices to the Vedas giving rules for the construction of altars— called the Baudhāyana Śulbasûtra, which contained several important mathematical results.
- 7. He is older than the other famous mathematician Āpastambha. He belongs to the Yajurveda school. He is accredited with calculating the value of pi before pythagoras, and with discovering what is now known as the Pythagorean theorem.
- 8. Baudhayana made the following constructions : 1)To draw a straight line at right angles to a given straight line. 2)To draw a straight line at right angles to a given straight line to a given point from it . 3)To construct a square having a given side. 4)To construct a rectangle of given sides. 5)To construct a isosceles trapezium of a given altitude, face and base.
- 9. 6)To construct a parallelogram having given sides at a given inclination. 7)To draw a square equivalent to n times a given square. 8)To draw a square equivalent to the sum of two different squares. 9)To draw a square equivalent to two given triangles. 10)To transform a rectangle into square.
- 10. 11)To transform a square into rectangle. 12)To transform a square into an rectangle which shall have an given side . 13)To transform a square or a rectangle into an triangle . 14)To transform a square into an rhombus. 15)To transform a rhombus into an square.
- 11. DRAWING ISOSCELES TRAPEZIUM • Draw two parallel line segments of equal length, say AB and CD. • Take P as midpoint of CD. • Join PA and PB. • Draw PM as altitude of ΔPAB.
- 12. • Consider a point Q on MP produced. • With the center at M and radius MQ, draw an arc of a circle, cutting line CD at points E and F. • Join AE and BF. • AEFB is an isosceles trapezium. DRAWING ISOSCELES TRAPEZIUM
- 13. DRAWING ISOSCELES TRAPEZIUM Proof : Δ APM and BPM are congruent. Also ME = MF = radius of circle. Therefore, Δ MEP are MFP are congruent. => Δ AEP and BFP are congruent. => AE = BF Therefore, trapezium is isosceles with two non parallel equal sides.
- 14. Thank U!!!