Lesson 4
GEOMETRIC CONSTRUCTION
GEOMETRIC CONSTRUCTION
W E L C O M E !
INTRODUCTION TO GEOMETRIC CONSTRUCTION
OBJECTIVES
define what is Geometric Construction and its importance,
relates Geometry to Drafting and;
construct Geometrical Figures
Many of the constructions used in technical design drawing are based upon plane geometry, and every draftsman or engineer should be sufficiently familiar with them to be apply them to the solutions of the problems. Pure geometry problems may be solved only with the compass and a straightedge, and in some cases these methods may be used to advantage in technical drawing. However, the draftsman or designer has available the T-square, triangles, dividers, and other equipment, such as drafting machines, that in many cases can yield accurate results more quickly by what we may term “preferred methods”.
Geometric construction is the process of drawing a geometrical figure using two geometrical instruments, a compass, and a ruler.
· We use a compass to draw arcs and circles and mark off equal lengths.
· We use a ruler to draw line segments and measure their lengths.
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Many students feel that Geometry is a challenging topic, while some even enjoy practicing this subject. However, there are several reasons behind teaching Geometry to students from an early age and the most important reason of all is its use in day-to-day life. Therefore, the students must understand this concept well.
1. Construction of Buildings
The best use of geometry in daily life is the construction of buildings, dams, rivers, roads, temples, etc. For ages, geometry has been exceptionally used to make temples that hold the heritage of our country. Some of these famous temples are even counted as miraculous developments done by people with primitive instruments.
2. Computer Graphics
The audiovisual presentation in different segments such as education, entertainment, etc. uses geometry as a part of the art and creativity. Computer graphics is a prime application of geometry in day-to-day life we can consider here. Smartphones, laptops, computers, etc. are designed using geometrical concepts. The games we play also use geometry to find relevance between the distance and shapes of objects designed.
3. Art
Another excellent use of geometry is how artists use the concepts to design the best paintings and express their ideologies. The use of colors, brushes, and different strokes give birth to excellent artwork. Artists also design apparel, accessories, and other items we use. You can understand the importance of geometry in daily life.
4. Measuring Orbits and Planetary Motions
This concept is used by astronomers to track stars, measure the orbits and distance between planets and satellites. Scientists also measure the factors and set the path of satellites launched. This is one of the best applications of coordinate geometry in daily life.
5. Interior Design
The applications of coordinate geometry in daily life can also be found in interior design. Setting new items in an open space is done perfectly using the concepts of coordinate geometry.
· Point
· Line
· Plane
· Solid
A theoretical location that has neither width, height, nor depth.
Describes exact location in space.
A point is represented in technical drawing as a small cross made of dashes that are approximately 3 mm long.
A geometric primitive that has length and direction, but no thickness.
It may be straight, curved or a combination of these.
Lines also have important relationship or conditions, such as parallel, intersecting, and tangent.
Lines – specific length and non-specific length.
Ray – Straight line that extends to infinity from a specified point.
• Given line AB and tangent point T. Construct a line perpendicular to line AB and through point T.
• Locate the center of the arc by making the radius on the perpendicular line. Put the point of the compass at the center of the arc, set the compass for the radius of the arc, and draw the arc which will be tangent to the line through the point T
Given the sides A, B, C, as shown:
I. Draw one side, as C, in desired position, and strike arc with radius equal equal to given side A.
II. Strike arc with radius equal to given side B.
III. Draw sides A and B from intersection of arcs, as shown.
Given side AB, as shown:
I. With A and B as centers and AB as radius strike arcs to intersect at C. Draw lines AC and BC to complete the triangle.
II. Draw lines through points A and B making angles of 60 degree with the given line and intersecting at C, as shown.
Given the circumscribed circle, as shown:
I. Divide the circumference of the circumference of the circle into five equal parts with the dividers, and join the points with straight lines.
II. Bisect radius OD at C.
III. With C as center, and CA as radius, strike arc AE. With A as center, and AE as radius, strike arc EB.
IV. Draw line AB; then set off distances AB around the circumference of the circle, and draw the sides through these points.
LEARNING ACTIVITY
REFERENCES:
CONTENT SOURCE:
Brown, W. C. (1994). Drafting for Industry /by Walter C. Brown. Goodheart-Willcox.
VIDEO SOURCE:
URL: https://youtu.be/-sTpRONtGWM
URL: https://youtu.be/D9UXfNc1ePs
URL: https://youtu.be/0ZvIvNTv5GU
URL: https://youtu.be/zL1BA-mcjcc