This document discusses three types of compositional techniques: triangles, diagonals, and horizontals. It presents compositional triangles, then moves on to discuss compositional diagonals, and finally covers compositional horizontals.
The document discusses concepts in solid geometry including:
- Classifying three-dimensional figures according to their properties such as polyhedra, prisms, pyramids, cylinders, and cones.
- Relating two-dimensional nets to their three-dimensional shapes.
- Analyzing cross-sections of three-dimensional shapes.
- Key terms such as faces, edges, vertices, altitude, Platonic solids, Euler's formula, and surface area are defined.
- Examples of describing three-dimensional shapes from their nets and calculating surface areas of prisms are provided.
This document discusses isometric projections and drawings. It defines the different types of axonometric projections including isometric, dimetric, and trimetric. Isometric projections have all angles equal, while dimetric has two equal angles and trimetric has none equal. The document explains how to construct isometric scales and draw isometric views using true lengths rather than foreshortened lengths. It also covers orienting the isometric axes and the steps for sketching objects in isometric views.
This document provides information about quadrilaterals in geometry. It defines a quadrilateral as a four-sided plane figure formed by joining four non-collinear points taken two at a time, which results in six lines including four sides and two diagonals. Quadrilaterals are classified as either convex or concave depending on whether the diagonals lie inside or outside the figure. Special types of quadrilaterals include parallelograms, rectangles, squares, rhombi, trapezoids, and kites based on their side and angle properties. The key properties are that the sum of the interior angles of any quadrilateral is always 360 degrees.
The document discusses various geometric shapes and artworks that use geometric elements. It provides definitions and examples of triangles, quadrilaterals, and polygons. Specific artworks mentioned include paintings by Josef Albers, Richard Anuszkiewicz, Antoni Tapies, Pablo Picasso, and Georges Braque. The document asks the reader to identify shapes in images, find examples of artworks using certain techniques, and define geometric terms.
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.
An isometric view shows all three dimensions of an object in a single view at 120 degree angles, allowing a non-technical viewer to understand the object's shape. Orthographic views only show two dimensions and are difficult for non-technical people to interpret. An isometric drawing is made by defining isometric axes intersecting at 120 degrees and drawing lines parallel to these axes. An isometric scale accounts for foreshortening of edges not viewed perpendicular and allows drawing accurate scaled isometric views from orthographic projections like plans and elevations. The steps are to define isometric axes, draw front face along them, add other faces and details, and use an isometric scale for a problem requiring a scaled isometric view from
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles in triangles. The key concepts are the trigonometric functions sine, cosine, and tangent, which describe ratios of sides of a right triangle. Trigonometry has applications in fields like navigation, music, engineering, and more. It has evolved significantly from its origins in ancient Greece and India, with modern definitions extending it to all real and complex number arguments.
PGL (Persamaan Garis Dari Gambar Garis Lurus & Dari Dua Titik) - Pertemuan 1Shinta Novianti
Pertemuan 1
BAB 4. Persamaan Garis Lurus (PGL)
Materi: PGL
Sub Materi: Persamaan Garis Dari Gambar Garis Lurus & Dari Dua Titik
MATEMATIKA
Kelas 8
TP 2021/2022
#jhs
#pjj
#sn
The document discusses concepts in solid geometry including:
- Classifying three-dimensional figures according to their properties such as polyhedra, prisms, pyramids, cylinders, and cones.
- Relating two-dimensional nets to their three-dimensional shapes.
- Analyzing cross-sections of three-dimensional shapes.
- Key terms such as faces, edges, vertices, altitude, Platonic solids, Euler's formula, and surface area are defined.
- Examples of describing three-dimensional shapes from their nets and calculating surface areas of prisms are provided.
This document discusses isometric projections and drawings. It defines the different types of axonometric projections including isometric, dimetric, and trimetric. Isometric projections have all angles equal, while dimetric has two equal angles and trimetric has none equal. The document explains how to construct isometric scales and draw isometric views using true lengths rather than foreshortened lengths. It also covers orienting the isometric axes and the steps for sketching objects in isometric views.
This document provides information about quadrilaterals in geometry. It defines a quadrilateral as a four-sided plane figure formed by joining four non-collinear points taken two at a time, which results in six lines including four sides and two diagonals. Quadrilaterals are classified as either convex or concave depending on whether the diagonals lie inside or outside the figure. Special types of quadrilaterals include parallelograms, rectangles, squares, rhombi, trapezoids, and kites based on their side and angle properties. The key properties are that the sum of the interior angles of any quadrilateral is always 360 degrees.
The document discusses various geometric shapes and artworks that use geometric elements. It provides definitions and examples of triangles, quadrilaterals, and polygons. Specific artworks mentioned include paintings by Josef Albers, Richard Anuszkiewicz, Antoni Tapies, Pablo Picasso, and Georges Braque. The document asks the reader to identify shapes in images, find examples of artworks using certain techniques, and define geometric terms.
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.
An isometric view shows all three dimensions of an object in a single view at 120 degree angles, allowing a non-technical viewer to understand the object's shape. Orthographic views only show two dimensions and are difficult for non-technical people to interpret. An isometric drawing is made by defining isometric axes intersecting at 120 degrees and drawing lines parallel to these axes. An isometric scale accounts for foreshortening of edges not viewed perpendicular and allows drawing accurate scaled isometric views from orthographic projections like plans and elevations. The steps are to define isometric axes, draw front face along them, add other faces and details, and use an isometric scale for a problem requiring a scaled isometric view from
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles in triangles. The key concepts are the trigonometric functions sine, cosine, and tangent, which describe ratios of sides of a right triangle. Trigonometry has applications in fields like navigation, music, engineering, and more. It has evolved significantly from its origins in ancient Greece and India, with modern definitions extending it to all real and complex number arguments.
PGL (Persamaan Garis Dari Gambar Garis Lurus & Dari Dua Titik) - Pertemuan 1Shinta Novianti
Pertemuan 1
BAB 4. Persamaan Garis Lurus (PGL)
Materi: PGL
Sub Materi: Persamaan Garis Dari Gambar Garis Lurus & Dari Dua Titik
MATEMATIKA
Kelas 8
TP 2021/2022
#jhs
#pjj
#sn
Trigonometry can be covered in 15 minutes by focusing on right triangles. The Pythagorean theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides. The sine, cosine, and tangent ratios relate the lengths of sides of a right triangle to an angle and do not depend on the triangle's size. Java's Math class contains methods for calculating trigonometric functions using radians as input. Memorizing the ratio names can be aided by mnemonics like "Some Old Horse Caught Another Horse Taking Oats Away".
This document provides information on isometric projection and isometric drawing. It defines isometric projection as a type of axonometric projection where all three axes are equally scaled at 120 degrees. Isometric drawings can be created using the box method, which involves sketching an imaginary box around the object and then removing volumes to draw the details. Key steps include positioning isometric axes, sketching the enclosing box, adding details while measuring on the axes, and darkening visible lines. Non-isometric lines that do not run parallel to the axes must be drawn using coordinate points on isometric lines. Circles appear as ellipses in isometric drawings and can be drawn using the four-center method.
The document provides information about trigonometry at the foundation and pass levels. At the foundation level, students should be able to solve problems using right-angled triangles, Pythagoras' theorem, and calculating trig functions between 0-90 degrees. At pass level, students must also be able to use trigonometry to calculate triangle area, use sine and cosine rules to solve 2D problems, define trig functions for all values, and calculate areas of circles and arcs. The document then explains how to graph trig functions like sine, cosine, and tangent, noting their periodic properties.
This document provides information on isometric projections and isometric drawing techniques. It discusses how isometric projections allow three faces of an object to be viewed at once by pivoting the object 45 degrees. It also describes how isometric drawings are created using a "box construction" method where measurement lines are drawn at 30 degree angles to form an outline box for the object. The stages of isometric drawing are outlined as sketching the box, measuring details, and final layout. Methods for drawing non-isometric lines, circles, and rounded objects in isometric perspective are also summarized.
The document discusses isometric projection, which is a method for visually representing three-dimensional objects in two dimensions in technical drawings. It defines key terms like isometric axes and lines. The steps for constructing an isometric projection are outlined, including defining the axes and adding details to blocks. Various types of objects that can be drawn using isometric projection are described, such as those with normal, oblique, or curved surfaces. Circles are approximated as ellipses, while curved lines use a series of offset points.
This document discusses isometric projection and how to draw isometric views of objects. It explains that isometric projection shows all three dimensions of an object using three intersecting axes at 120 degree angles. True dimensions are used for isometric views of single solids, while isometric projections of combinations of solids use compressed isometric dimensions. Common techniques for drawing isometric views, like the box method and 4-center method for circles, are described. Several step-by-step examples demonstrate how to apply these techniques to draw isometric views of prisms, cylinders, and cut pyramids. Tips are provided on what details to include or omit in isometric drawings.
Trigonometry is the branch of mathematics that deals with triangles and relationships between sides and angles. It was originally developed to solve geometric problems involving triangles. Key concepts in trigonometry include trigonometric ratios such as sine, cosine, and tangent that relate angles and sides of a right triangle. Trigonometry is used in many fields including architecture, engineering, astronomy, music and more. It allows calculations of heights, distances, and positions that are important for applications like building design, navigation, and satellite positioning.
This document provides information about similar triangles over 5 pages. It begins by defining similar figures and triangles, and explaining the properties of similar triangles including equal corresponding angles and proportional corresponding sides. It then lists various criteria and properties to determine if triangles are similar, such as AAA, SSS, and angle-side criteria. The document concludes with 50 multiple choice questions related to similar triangles.
Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
Topics:-
Intro, Information, Formulas, Summary and overview
This document provides an overview of trigonometry, including its origins in Greek mathematics, the six main trigonometric functions defined in terms of right triangles, and trigonometric identities. Trigonometry is the study of triangles and relationships between sides and angles, with the six functions—sine, cosine, tangent, cotangent, secant, and cosecant—defined based on ratios of sides. Special angle values and identities are also discussed as important concepts in trigonometry.
The document provides instructions for drawing the perspective of an open book with 6 pages labeled A through F at varying angles:
1) Establish the end view, plan, picture plane, station point, horizon line, and ground line.
2) Determine the left and right vanishing points where lines from the station point intersect the picture plane.
3) Find the auxiliary vanishing points for pages at 30 and 60 degrees by drawing lines at those angles and intersecting the picture plane.
4) Use the vanishing points and auxiliary points to draw the book's edges and pages in correct perspective.
The concept of trigonometric ratios is important in Maths trigonometry. Some of applications and procedures are discussed here for easy understanding the concept clarity.
Trigonometric ratios relate the sides of a right triangle to an angle of the triangle. When a point P lies on a circle of radius r, the line segments from P to the center O and x-axis form a right triangle. The trigonometric ratios are defined as the ratio of an opposite, adjacent, or hypotenuse side to the hypotenuse. For example, sine is the ratio of the opposite side to the hypotenuse. Reciprocal trigonometric functions can also be defined, with sine and cosecant being reciprocals of each other.
Math lecture 8 (Introduction to Trigonometry)Osama Zahid
Trigonometry involves calculating relationships between sides and angles of triangles. The main trigonometric functions are sine, cosine, and tangent, which relate the opposite, adjacent, and hypotenuse sides to an angle. These functions repeat in a repeating pattern as angles increase or decrease by full rotations. Trigonometry is used to solve for unknown sides and angles of triangles.
this is a slide share on introduction of trigonometry this slide share includes every single information about the lesson trigonometry and this is best for class 10
Steps in constructing an isometric drawingRodolfo Aquino
The document outlines the 7 steps to construct an isometric drawing: 1) Draw the three axes at 30 degrees, 2) Plot the principal dimensions of Height, Width, and Depth, 3) Draw the outer lines of the object lightly, 4) Add the internal details by analyzing points, 5) Check the accuracy, 6) Trace visible edges with darker lines, 7) Label the drawing. It also lists 4 key points to remember like keeping axes equally spaced at 120 degrees and using light lines initially.
This document provides information and examples regarding isometric projection drawings. It defines key terms like isometric axes, lines, and planes. It explains that in isometric projection, all three dimensions are shown in one view at equal 120 degree angles between axes. It provides instructions for constructing isometric scales and converting true lengths to reduced isometric lengths. It includes examples of how to draw isometric views of various objects like prisms, pyramids, cylinders, and spherical objects. It also provides practice problems drawing isometric views given orthographic projections as input.
Additive color is the process of combining different amounts of red, green, and blue light to reproduce a broad range of colors. This is how color displays like computer monitors and televisions work. Subtractive color is the opposite and involves combining pigments or dyes to filter or subtract certain wavelengths of light, which is how color printing and painting with physical materials works.
Tint, Shade, Tone, Color Harmonies, and the Interaction of ColorZwanita
This document discusses different aspects of color including tints, shades, tones, color harmonies, and the interaction of colors. It explores how colors can be lightened or darkened through the use of tints and shades, and modified through tones. It also examines color harmonies and how different colors relate to and influence one another.
Trigonometry can be covered in 15 minutes by focusing on right triangles. The Pythagorean theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides. The sine, cosine, and tangent ratios relate the lengths of sides of a right triangle to an angle and do not depend on the triangle's size. Java's Math class contains methods for calculating trigonometric functions using radians as input. Memorizing the ratio names can be aided by mnemonics like "Some Old Horse Caught Another Horse Taking Oats Away".
This document provides information on isometric projection and isometric drawing. It defines isometric projection as a type of axonometric projection where all three axes are equally scaled at 120 degrees. Isometric drawings can be created using the box method, which involves sketching an imaginary box around the object and then removing volumes to draw the details. Key steps include positioning isometric axes, sketching the enclosing box, adding details while measuring on the axes, and darkening visible lines. Non-isometric lines that do not run parallel to the axes must be drawn using coordinate points on isometric lines. Circles appear as ellipses in isometric drawings and can be drawn using the four-center method.
The document provides information about trigonometry at the foundation and pass levels. At the foundation level, students should be able to solve problems using right-angled triangles, Pythagoras' theorem, and calculating trig functions between 0-90 degrees. At pass level, students must also be able to use trigonometry to calculate triangle area, use sine and cosine rules to solve 2D problems, define trig functions for all values, and calculate areas of circles and arcs. The document then explains how to graph trig functions like sine, cosine, and tangent, noting their periodic properties.
This document provides information on isometric projections and isometric drawing techniques. It discusses how isometric projections allow three faces of an object to be viewed at once by pivoting the object 45 degrees. It also describes how isometric drawings are created using a "box construction" method where measurement lines are drawn at 30 degree angles to form an outline box for the object. The stages of isometric drawing are outlined as sketching the box, measuring details, and final layout. Methods for drawing non-isometric lines, circles, and rounded objects in isometric perspective are also summarized.
The document discusses isometric projection, which is a method for visually representing three-dimensional objects in two dimensions in technical drawings. It defines key terms like isometric axes and lines. The steps for constructing an isometric projection are outlined, including defining the axes and adding details to blocks. Various types of objects that can be drawn using isometric projection are described, such as those with normal, oblique, or curved surfaces. Circles are approximated as ellipses, while curved lines use a series of offset points.
This document discusses isometric projection and how to draw isometric views of objects. It explains that isometric projection shows all three dimensions of an object using three intersecting axes at 120 degree angles. True dimensions are used for isometric views of single solids, while isometric projections of combinations of solids use compressed isometric dimensions. Common techniques for drawing isometric views, like the box method and 4-center method for circles, are described. Several step-by-step examples demonstrate how to apply these techniques to draw isometric views of prisms, cylinders, and cut pyramids. Tips are provided on what details to include or omit in isometric drawings.
Trigonometry is the branch of mathematics that deals with triangles and relationships between sides and angles. It was originally developed to solve geometric problems involving triangles. Key concepts in trigonometry include trigonometric ratios such as sine, cosine, and tangent that relate angles and sides of a right triangle. Trigonometry is used in many fields including architecture, engineering, astronomy, music and more. It allows calculations of heights, distances, and positions that are important for applications like building design, navigation, and satellite positioning.
This document provides information about similar triangles over 5 pages. It begins by defining similar figures and triangles, and explaining the properties of similar triangles including equal corresponding angles and proportional corresponding sides. It then lists various criteria and properties to determine if triangles are similar, such as AAA, SSS, and angle-side criteria. The document concludes with 50 multiple choice questions related to similar triangles.
Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
Topics:-
Intro, Information, Formulas, Summary and overview
This document provides an overview of trigonometry, including its origins in Greek mathematics, the six main trigonometric functions defined in terms of right triangles, and trigonometric identities. Trigonometry is the study of triangles and relationships between sides and angles, with the six functions—sine, cosine, tangent, cotangent, secant, and cosecant—defined based on ratios of sides. Special angle values and identities are also discussed as important concepts in trigonometry.
The document provides instructions for drawing the perspective of an open book with 6 pages labeled A through F at varying angles:
1) Establish the end view, plan, picture plane, station point, horizon line, and ground line.
2) Determine the left and right vanishing points where lines from the station point intersect the picture plane.
3) Find the auxiliary vanishing points for pages at 30 and 60 degrees by drawing lines at those angles and intersecting the picture plane.
4) Use the vanishing points and auxiliary points to draw the book's edges and pages in correct perspective.
The concept of trigonometric ratios is important in Maths trigonometry. Some of applications and procedures are discussed here for easy understanding the concept clarity.
Trigonometric ratios relate the sides of a right triangle to an angle of the triangle. When a point P lies on a circle of radius r, the line segments from P to the center O and x-axis form a right triangle. The trigonometric ratios are defined as the ratio of an opposite, adjacent, or hypotenuse side to the hypotenuse. For example, sine is the ratio of the opposite side to the hypotenuse. Reciprocal trigonometric functions can also be defined, with sine and cosecant being reciprocals of each other.
Math lecture 8 (Introduction to Trigonometry)Osama Zahid
Trigonometry involves calculating relationships between sides and angles of triangles. The main trigonometric functions are sine, cosine, and tangent, which relate the opposite, adjacent, and hypotenuse sides to an angle. These functions repeat in a repeating pattern as angles increase or decrease by full rotations. Trigonometry is used to solve for unknown sides and angles of triangles.
this is a slide share on introduction of trigonometry this slide share includes every single information about the lesson trigonometry and this is best for class 10
Steps in constructing an isometric drawingRodolfo Aquino
The document outlines the 7 steps to construct an isometric drawing: 1) Draw the three axes at 30 degrees, 2) Plot the principal dimensions of Height, Width, and Depth, 3) Draw the outer lines of the object lightly, 4) Add the internal details by analyzing points, 5) Check the accuracy, 6) Trace visible edges with darker lines, 7) Label the drawing. It also lists 4 key points to remember like keeping axes equally spaced at 120 degrees and using light lines initially.
This document provides information and examples regarding isometric projection drawings. It defines key terms like isometric axes, lines, and planes. It explains that in isometric projection, all three dimensions are shown in one view at equal 120 degree angles between axes. It provides instructions for constructing isometric scales and converting true lengths to reduced isometric lengths. It includes examples of how to draw isometric views of various objects like prisms, pyramids, cylinders, and spherical objects. It also provides practice problems drawing isometric views given orthographic projections as input.
Additive color is the process of combining different amounts of red, green, and blue light to reproduce a broad range of colors. This is how color displays like computer monitors and televisions work. Subtractive color is the opposite and involves combining pigments or dyes to filter or subtract certain wavelengths of light, which is how color printing and painting with physical materials works.
Tint, Shade, Tone, Color Harmonies, and the Interaction of ColorZwanita
This document discusses different aspects of color including tints, shades, tones, color harmonies, and the interaction of colors. It explores how colors can be lightened or darkened through the use of tints and shades, and modified through tones. It also examines color harmonies and how different colors relate to and influence one another.
Saturation refers to the purity of a color, ranging from bright and full to dull and gray. Highly saturated colors are medium in value and bright, meaning they are neither very light nor very dark but have an intense, pure hue. Unsaturated colors have less purity and appear more gray.
This document contains contact information for Amelia Carley. It lists her name and includes a website URL, www.ameliacarley.com. The document provides basic identifying information for Amelia Carley but does not include any other details about her or her work.
Color is an important element in visual communication. Different colors can elicit different emotional responses. Red is often associated with danger or excitement, while blue is commonly linked to feelings of calmness and security.
Nature of light, Lighting Tools and The Color WheelZwanita
Light can be understood as a wave or particle that travels in straight lines and interacts with matter to produce illumination and color. Various tools like lamps, flashlights, and light bulbs are used to produce and direct light for lighting needs. The color wheel is a visual representation of additive and subtractive color mixing which shows the relationships between primary, secondary, and tertiary colors.
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.
This document discusses compositional techniques for visual art and photography. It mentions positive and negative space as well as the rule of thirds, which involves dividing the frame into thirds both horizontally and vertically to place subjects of interest at the intersections. The golden mean is also referenced, which involves positioning elements in an asymmetrical but visually pleasing arrangement.
This document discusses different types of frames including open frames which have no sides, closed frames which are fully enclosed, frames within frames where one frame is contained inside another larger frame, and balanced and unbalanced frames where balanced frames have equal elements on both sides and unbalanced frames do not.
Henri Matisse created colorful paper cut-outs in his later years, when he was confined to a wheelchair due to health problems. Using sheets of colored paper and scissors, Matisse cut paper into shapes, curves, and motifs to create vibrant collages and individual designs. The cut-outs demonstrated Matisse's continuing exploration of color, form, and artistic experimentation even late in his life.
This short document discusses three key aspects of filmmaking: the frame, aspect ratio, and organic unity. It seems to be about the technical and compositional elements that filmmakers use to present their story and message in a cohesive visual format.
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.
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.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
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 boost feelings of calmness, happiness and focus.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
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.
Boudoir photography, a genre that captures intimate and sensual images of individuals, has experienced significant transformation over the years, particularly in New York City (NYC). Known for its diversity and vibrant arts scene, NYC has been a hub for the evolution of various art forms, including boudoir photography. This article delves into the historical background, cultural significance, technological advancements, and the contemporary landscape of boudoir photography in NYC.
This tutorial offers a step-by-step guide on how to effectively use Pinterest. It covers the basics such as account creation and navigation, as well as advanced techniques including creating eye-catching pins and optimizing your profile. The tutorial also explores collaboration and networking on the platform. With visual illustrations and clear instructions, this tutorial will equip you with the skills to navigate Pinterest confidently and achieve your goals.