Geometry 1_joints method

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
CONTENT
50%
GEOMETRY
25%
MATRICES
25%
THEORY
INTRODUCTORY
COURSE
5 DAYS
10 DAYS 6 DAYS 4 DAYS

4. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
PREVIOUSLY ON MATHS 1...

5. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
LEARNING PROCESS
HOW TO PASS
WHERE AM I?
Question of the day = First minute question
Class work quiz
GEOMETRY: VECTORS

6. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
LEARNING PROCCESS
LEARNING by DOING
INDUCTION: EXERCISES (buildings) and then, in the end, THEORY
WORK IN CLASS EVERY DAY
REVIEW THE EXERCISES AT HOME EVERY DAY
ASK EVERY QUESTION YOU HAVE
ARRIVE ON TIME Question of the day
Class work quiz

7. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HOW TO PASS WORKING in CLASS (and at home) EVERYDAY

8. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HOW TO PASS
CW = Class work FE = Final Exam RETAKE
CW1 = Class work PART 1
CW2 = Class work PART 2
CW3 = Class work PART 3
FE1 = Final Exam PART 1
FE2 = Final Exam PART 2
FE3 = Final Exam PART 3
PASS = FINAL GRADE = 0,5 x Max (CW1,FE1) + 0,25 x Max (CW2,FE2) + 0,25 x Max (CW3,FE3) > 5,0
PASS RETAKE = 0,5 x Retake part 1 + 0,25 x Retake part 2 + 0,25 x Retake part 3
Retake part 1
Retake part 2
Retake part 3
WORKING in CLASS (and at home) EVERYDAY

9. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HOW TO PASS
CW = Class work FE = Final Exam RETAKE
CW1 = Class work PART 1
CW2 = Class work PART 2
CW3 = Class work PART 3
FE1 = Final Exam PART 1
FE2 = Final Exam PART 2
FE3 = Final Exam PART 3
PASS = FINAL GRADE = 0,5 x Max (CW1,FE1) + 0,25 x Max (CW2,FE2) + 0,25 x Max (CW3,FE3) > 5,0
PASS RETAKE = 0,5 x Retake part 1 + 0,25 x Retake part 2 + 0,25 x Retake part 3
Retake part 1
Retake part 2
Retake part 3
WORKING in CLASS (and at home) EVERYDAY

10. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HOW TO PASS
EXTRA BONUS FOR ARRIVING ON TIME
FIRST MINUTE QUESTIONS
If you are in and you answer correctly
10 POINTS
If you are in and you answer wrong
5 POINTS
If you are not in
0 POINTS

11. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HOW TO PASS
CW = Class work FE = Final Exam RETAKE
CW1 = Class work PART 1
CW2 = Class work PART 2
CW3 = Class work PART 3
FE1 = Final Exam PART 1
FE2 = Final Exam PART 2
FE3 = Final Exam PART 3
PASS = FINAL GRADE = 0,5 x Max (CW1,FE1) + 0,25 x Max (CW2,FE2) + 0,25 x Max (CW3,FE3) > 5,0
PASS RETAKE = 0,5 x Retake part 1 + 0,25 x Retake part 2 + 0,25 x Retake part 3
Retake part 1
Retake part 2
Retake part 3
WORKING in CLASS (and at home) EVERYDAY
The worst of each might be substituted by the
First Minute Questions average grade

12. 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

13. FIRST MINUTE QUESTION
ABOUT THE FIRST MINUTE QUESTION...
Which of the following sentences is true?
Answering it right gives 0 points
A
Answering it wrong gives 0 points
B
Not answering gives 0 points
C
All the answers are incorrect
D

14. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WHERE AM I?

15. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Find the value of the unknown angles of the figure beside if the
triangle is isosceles with an angle 100º

16. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Determine the length of sides A and C in the triangle of the
figure beside.

17. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Determine the lengths of segments A and B

18. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Determine the value of X

19. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Given the following equations systems: write them down using
matrix notation, compute the value of the matrix coefficients
determinant and find out the value of x and y.

20. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Given the following equations systems: write them down using
matrix notation, compute the value of the matrix coefficients
determinant and find out the value of x and y.

21. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Given the following equations systems: write them down using
matrix notation, compute the value of the matrix coefficients
determinant and find out the value of x and y.

22. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Find the roots or zeros of the equation:

23. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Compute the derivative of the function:

24. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Compute the definite integral of the function:

25. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
LEARNING PROCESS
HOW TO PASS
WHERE AM I?
Question of the day = First minute question
Class work quiz
GEOMETRY: VECTORS

26. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WHAT IS A VECTOR?
Object that has both a magnitude and a direction.
The direction of the vector is determined by its orientation and its sense
The magnitude is the length of the vector.

27. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WHAT IS A VECTOR?
Object that has both a magnitude and a direction.
The direction of the vector is determined by its orientation and its sense
The orientation tells us the angle the vector makes with the cartesian coordinate axes
The magnitude is the length of the vector.
It is really useful to compute the dimension of the projections X, Y and Z of a vector

28. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ADDITION OF VECTORS
IS THE MAGNITUDE OF a+b DIRECTLY THE ADDITION OF THE MAGNITUDES OF vector a AND vector b?
PARALLELOGRAM LAW (or Triangle Law)

29. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ADDITION OF VECTORS
PARALLELOGRAM LAW (or Triangle Law)
MAGNITUDE OF vector c?

30. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ADDITION OF VECTORS
MAGNITUDE OF VECTOR a+b+c+d?
BE CAREFUL WITH THE SIGNS!!!!

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

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

33. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Bligh Lobb Sports Architecture
Millennium Stadium - Cardiff, UK – 1999 - [Bligh Lobb Sports Architecture

34. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Millennium Stadium - Cardiff, UK – 1999 - [Bligh Lobb Sports Architecture

35. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
The figure below is a simplified model of part of the structural system of the Cardiff
Millennium Stadium. Determine the sign and value of the forces at every bar.
*Assume all the forces have the direction of the bars.
*Assume every joint is in equilibibrium (addition of forces at each joint equals zero)

36. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
1.- How can I start?
2.- Do not forget: the magnitude is not enough!

37. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT B

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

39. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT E

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

41. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT F

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

43. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT A

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

45. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT C

46. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT C

47. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT D

48. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT D

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

50. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
BE ORGANIZED!!!!
WATCH OUT THE SIGNS!!!!

51. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Today’s words?
https://www.menti.com/8cwme7e7ux
https://www.mentimeter.com/app

52. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Bridge in Rodó Park. Tacuarembó. Uruguay

53. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
The figure below is a simplified model of the Bridge in Rodó Park,
Tacuarembó, Uruguay. Determine the sign and value of the forces at
every bar.
*Assume all the forces have the direction of the bars.
*Assume every joint is in equilibibrium (addition of forces at each joint
equals zero)