UNIT 2: OPERATIONS WITH LINE SEGMENTS

2. Operations with Line Segments

2.1. Adding and subtracting line segments

       a) Adding

•  The addition of two segments is another segment that begins at the origin of the first segment and ends  at   the end of the second segment. 
• The length of the new segment is the addition of the measures of those two segments.

      b) Subtrating

• The subtration of two segments is another segment that takes as the origin, the end of the smaller segment and as the end, the end of the biggest segment.
• The length of the segment difference is equal to the subtraction of the lengths of two segments.

 

2.2. Line Bisector

• The line bisector is a perpendicular line that passes through the midpoint of the segment, so it divides the segment in two equal parts.

THEORY EXTRA (NOT FOR THE ARTBOOK)

2.3. How to divide a line segment into equal parts (Thales theorem)

1. Draw a ray that shares the origin of point A with the line segment segment AB.

 

2. Mark in the ray as many equal units as you want to obtain starting from point A. In this case, we are goint to divide the segment into three equal parts.

 

3. Join the point B with the end of the ray. For each of the divisions of the ray, draw parallel lines to the segment joining B. The points obtained in the segment AB represent 3 equal parts.

 

If you have any doubt about the process, you can watch theses videos:

 

UNIT 2: PARALLEL AND PERPENDICULAR LINES, SET SQUARE RULERS.

UNIT 2: PARALLEL  AND PERPENDICULAR LINES, SET SQUARE RULERS. 

These are a few videos to give you information about parallel, perpendicular and intersecting lines and how to draw them using the set square rulers. Then feel free to get artistic!!! 

DEFINITIONS:  

PARALLEL LINES are lines that never join or meet. 

PERPENDICULAR LINES are lines that join or meet making 90º angles (right angles)

SET SQUARE RULERS

                 45º Set Square Ruler (Escuadra)                                 60º-30º Set Square Ruler (Cartabón)

How do we use the set square?

You have to handle your set square softly and with accuracy without exercising too much pressure on them, only the needed one to avoid movement.

PARALLEL LINES are lines that never join. 

HOW TO DRAW PARALLEL LINES

1. The 45 set square hypotenuse (longest side) is placed attached to the line to which we want to draw the parallels (GUIDE).
2. The 60-30 set square hypotenuse is attached to the 45 set square leg.
3. Fix the 60-30 set square and move the 45 set square upwards or downwards drawing the desired parallel lines along its hypotenuse.

PERPENDICULAR LINES are lines that join making 90º angles (right angles)

HOW TO DRAW PERPENDICULAR LINES

If we want to draw perpendicular lines to one direction, we will have to follow the first two steps as stated for parallel lines and then the following ones:

1. Having fixed the 60-30 set square, the 45 set square is turned until the other leg is attached to the hypotenuse of the 60-30 set square.
2. Draw the perpendicular line along the hypotenuse of the 45 set square.

Let's review how to draw parallel and perpendicular lines using the triangular set squares.

UNIT 1: INTRODUCTION TO GEOMETRY.

INTRODUCTION: Geometry, Nature and Art. 

THE MAGIC OF GEOMETRY

Here are a few videos that show wonderfully the way Nature, Geometry and Art blend together. The three are interconnected. One can not fully exist without the other. 

 "NATURE BY NUMBERS" (Golden Ratio, and the Fibonacci Seies) a 3D animated short film by Cristobal Vila. 

"INFINITE PATTERNS" also by Cristobal Vila. 

"MATES APLICADAS" by José Ramón Soriano.