3. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
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4. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
LINES IN A TWO DIMENSION COORDINATE SYSTEM (LINES IN 2D OR CONTAINED IN A PLANE)
EXAMPLE 5. POSITION and FORCES MAGNITUDES
LINES point + vector director
LINES explicit equation
LINES implicit equation
INTRODUCTORY CONCEPTS
5. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FIRST MINUTE QUESTION
Username: First part of your CEU email
For example:
if your email is a.garcia245@uspceu.es
Your username will be a.garcia245
Password: SAME AS USERNAME
6. FIRST MINUTE QUESTION
Which of these sentences is true?
AB force should be smaller than BC force
A
B
C
D All the sentences are false
AB slope should be bigger than BC slope
AB force should be equal than BC force
8. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
INTRODUCTORY CONCEPTS
A POINT in geometry is a location.
It has no size no width, no length and no depth.
A point is shown by a dot.
A LINE is defined as a line of points that extends infinitely in two
directions. It has one dimension, length.
A plane extends infinitely in two dimensions. It has no thickness.
An example of a plane is a coordinate plane.
13. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
A POSITION VECTOR or RADIUS VECTOR
defines the position of a point
WE MUST DEFINE THE POSITION OF POINTS
14. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
¿POSITION VECTORS of A and B?
15. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
WE MUST DEFINE THE EQUATION OF LINES
WE WANT TO KNOW THE POSITION OF EVERY POINT OF THE LINE PARALLEL TO d that contains P
16. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
WE MUST DEFINE THE EQUATION OF LINES
WE WANT TO KNOW THE POSITION OF EVERY POINT OF THE LINE PARALLEL TO d that contains P
17. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
WE MUST DEFINE THE EQUATION OF LINES
WE WANT TO KNOW THE POSITION OF EVERY POINT OF THE LINE PARALLEL TO d that contains P
18. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
WE MUST DEFINE THE EQUATION OF LINES
WE WANT TO KNOW THE POSITION OF EVERY POINT OF THE LINE PARALLEL TO d that contains P
19. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE MUST DEFINE THE EQUATION OF LINES
WE WANT TO KNOW THE POSITION OF EVERY POINT OF THE LINE PARALLEL TO d that contains P
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
20. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE MUST DEFINE THE EQUATION OF LINES
WE WANT TO KNOW THE POSITION OF EVERY POINT OF THE LINE PARALLEL TO d that contains P
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
21. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
WE MUST DEFINE THE EQUATION OF LINES
22. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
WE MUST DEFINE THE EQUATION OF LINES
23. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO POINTS
• Or a POINT and the line VECTOR DIRECTOR
A VECTOR DIRECTOR of a straight line
is any vector that has the same direction
as the given straight line.
WE MUST DEFINE THE EQUATION OF LINES
24. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE MUST DEFINE THE EQUATION OF LINES
25. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE MUST DEFINE THE EQUATION OF LINES
26. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE MUST DEFINE THE EQUATION OF LINES
