3. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
PREVIOUSLY ON MATHS 1...
4. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
LINES IN A 3 DIMENSION COORDINATE SYSTEM (LINES CONTAINED IN SPACE)
LINES EQUATION point + vector director
LINES explicit equation
LINES implicit equation (vector director calculation)
DISTANCE between two points
DISTANCE between a point and a line
ANGLE between two lines
DOT PRODUCT, CROSS PRODUCT, TRIPLE PRODUCT
PARALLEL LINES, INTERSECTING LINES, SKEW LINES
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 FALSE?
The vector director of line r is (0, 8, 2)
A
B
C
D All the sentences are false
x = 4 in every point of line s
The distance between S and P is equal than between S and Q
13. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO EQUATIONS
(two planes that intersect)
• Or a POINT and the line VECTOR DIRECTOR
IN 3D, as i 2D, a line can be defined by:
14. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
• A line can be defined by TWO EQUATIONS
(two planes that intersect)
• Or a POINT and the line VECTOR DIRECTOR
IN 3D, as i 2D, a line can be defined by:
15. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
DOT PRODUCT
WHAT DOES IT MEAN THAT THE DOT PRODUCT BETWEEN TWO POINTS IS ZERO?
16. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
CROSS PRODUCT
17. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
TRIPLE PRODUCT
18. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
RELATIVE POSITION OF TWO LINES:
COINCIDENT LINES: same direction, all points in common.
PARALLEL LINES: same direction, no points in common.
They define a plane (coplanar lines).
LINES THAT INTERSECT: different direction, one point in common.
They define a plane (coplanar lines)
SKEW LINES: different direction, no points in common.
They do not define a plane (no coplanar lines)
19. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
RELATIVE POSITION OF TWO LINES:
COINCIDENT LINES: same direction, all points in common.
PARALLEL LINES: same direction, no points in common.
They define a plane (coplanar lines).
LINES THAT INTERSECT: different direction, one point in common.
They define a plane (coplanar lines)
SKEW LINES: different direction, no points in common.
They do not define a plane (no coplanar lines)
HOW CAN WE KNOW WHAT HAPPENS WITH NUMBERS?
20. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
PARALLEL LINES:
21. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
INTERSECTING LINES:
Lines intersect
Skew lines
Lines intersect Skew lines
22. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
LINE THAT INCLUDES TWO POINTS:
23. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MIDPOINT, DISTANCE BETWEEN TWO POINTS:
24. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
DISTANCE FROM A POINT TO A LINE
R is a point that belongs to line r
d is the vector director of the line r
25. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
DISTANCE BETWEEN TWO LINES
R is a point that belongs to line r
S is a point that belongs to line s
dr and ds are the vectors director of the lines r and s
26. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
DISTANCE BETWEEN TWO LINES
27. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ANGLE BETWEEN TWO LINES:
28. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ANGLE BETWEEN TWO LINES:
