LINE EQUATIONS_TRIANGLES

1. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTALS OF MATHEMATICS I

2. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

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 TWO DIMENSION COORDINATE SYSTEM (LINES IN 2D OR CONTAINED IN A PLANE)
LINES EQUATION point + vector director
LINES explicit equation
LINES implicit equation (SLOPE and intersection with the Y coordinate axis)
DISTANCE between two points
DISTANCE between a point and a line
ANGLE between two lines
TRIANGLES

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
If B and D were 400 and C were 300
AB slope would be bigger than BC slope
A
B
C
D All the sentences are false
AB force would be the same
The shape of the funicular diagram will not change

7. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

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.

9. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
TAICHUNG OPERA HOUSE. Taiwán. TOYO ITO. 2009-2016

10. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
TAICHUNG OPERA HOUSE. Taiwán. TOYO ITO. 2009-2016

11. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

12. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

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.
PARAMETRIC EQUATION

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.
CONTINUOUS EQUATION

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
WE MUST DEFINE THE EQUATION OF LINES
IMPLICIT EQUATION

24. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE MUST DEFINE THE EQUATION OF LINES
EXPLICIT EQUATION

25. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE MUST DEFINE THE EQUATION OF LINES
EXPLICIT EQUATION
IMPLICIT EQUATION

26. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

27. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

28. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

29. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

30. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

31. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

32. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

33. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Equation of the line that includes A and B?

34. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Equation of the line that forms 45º with r
and includes A?

35. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

36. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

37. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

38. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

39. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

40. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

41. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

42. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

43. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

44. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

45. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

46. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Today’s words?

47. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
YALE UNIVERSITY ART GALLERY
Louis Kahn 1947-1953

48. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
YALE UNIVERSITY ART GALLERY
Louis Kahn 1947-1953