1. Geometry with Mr. Young C-30, C-32
Welcome Generals!
Geometry with Mr. Young
C-30, C-32

2. Agenda Introductions Transformations Team work strategies
Mathematical art

3. Drawing task
You should all have a piece of plan white paper, straight edge, and pen or pencil. Pencil is preferred, though not required for this rough draft
We are going to do some art! Please look at, as well as read/listen to the directions.

4. Linear Perspective Drawings
3 Point Perspective
2 Point Perspective
1 Point Perspective
Linear Perspective Drawings

5. One-point perspective
One-point perspective

6. Using the X,Y,Z axis to draw
One Point Perspective

7. Examples Paintings with One Point Perspective
by G. Smith
Examples Paintings with One Point Perspective
by Canaletto

8. Two point perspective

9. Using the X,Y,Z axis to Plot Points in a
Two Point Perspective Painting Z X Y

10. Two Point Perspective Paintings

11. Three point perspective
3rd Vanishing point above if want sense of looking from above
3rd Vanishing point below if want sense of looking from below

12. Focusing on Two Perspective

13. Learning to Draw Two Point Perspective

14. Step 1: Draw line lightly across paper about 3 inches down from top
Step 1: Draw line lightly across paper about 3 inches down from top. We will call this the horizon.

15. Step 2: Make a small light dash on the horizon, about a 1/2 inch in from the edge of the paper. These are the vanishing points.

16. Step 3:make the z-axis – Place it off center
Step 3:make the z-axis – Place it off center. Extend the z line so there is about an inch at the top of the page and slightly more at the bottom. Z

17. Step 4:make the x-axis - from the bottom of z to the right hand vanishing point

18. Step 5:make the y-axis - from the bottom of z to the other vanishing point.

19. Step 6:make a light line from the top of the x-axis to the top of the z-axisy x

20. Step 7:make a light line from the top of the y-axis to the top of the z-axis

21. Step 8:Make two vertical lines - one on each side of the z-axis
Step 8:Make two vertical lines - one on each side of the z-axis. Notice they connect the two diagonal lines in your drawing. Z y x

22. Step 9:Darken the lines connecting to z-axis to the vertical lines just drawn.y x

23. Step 10:Draw a line part way up from the y-axis
Step 10:Draw a line part way up from the y-axis. It needs to go above the horizon. Z y x

24. Step 11:Lightly Connect the new vertical line to the vanishing point and add another vertical line, near the first, extending from the new diagonal line. Z y x

25. Step 12: Darken the line just drawn, but only the part between the two new vertical lines.Z y x

26. Step 13:Lightly Draw another line from the vanishing point to a spot above the last vertical line you made. Extend and darken the vertical line to this diagonal. Z y x

27. Step 14. Add a diagonal to the vanishing point from the last vertical you drew. Then add one more vertical line connecting the diagonal. Darken the vertical and the diagonal line between the two verticals. Z y x

28. Step 15:Draw a light line from the x vanishing point to the top of the middle two vertical lines. (see picture) Z y x

29. Step 16:Darken the newly drawn lines up until they hit the next vertical line.Z y x

30. Step 17:erase the light lines between the x and y axis.Z y x

31. Step 18. Add a vertical line on the x-axis, connect the top of the line to both vanishing points. Extend a 2nd vertical line from the diagonal from X. Darken the vertical lines and the diagonal between them.Also darken the diagonal towards Y until you run into an existing dark line. (see picture) Z y x

32. Step 19:darken lines between buildings.Z y x

33. Step 20:Erase light lines and put in line from the bottom of the 3rd vertical from y, to the x vanishing point. Also add a diagonal from the bottom of the 2nd vertical from X to the Y vanishing point. (see picture) Z y x

34. Step 21:Darken the lines you just made from the bottom of the building till it hits the next building Z y x

35. Step 22:choose where your sun goes and begin shading and adding more detail.Z y x

36. Put in the details….
This is not the building layout you drew, but it’s similar. Notice the are windows are vertical lines to the axes, and diagonal lines to the vanishing points, same for the doors and signs.

37. Homework
Create a two point perspective drawing of your house/apartment/street, or some other location that has meaning to you.
Write your name, class period, and location you chose to draw on the back of the drawings, as we may display the drawings in the classroom or hallway.
This, and all homework, will be due at the beginning of the next class. Homework amounts to about 15% of your total grade- but is critical to your success.

38. Warm – Up: No calculators
1) Solve: 2𝑥−3 = 15𝑥+8−2𝑥
2) Evaluate: 𝑏2 − 3 for 𝑏 = − 4
3) Simplify: 42 ÷ 2 ∗ 4 – (2 + 7)
4) Factor: 2 𝑥 2 +𝑥−15
5) Solve for m: 3𝑚 + 6𝑥 = 12
6) What are you going to learn in geometry this year?
𝒙=−𝟏 𝟏𝟑 𝟐𝟑
(𝟐𝒙−𝟓)(𝒙+𝟑)
Michael & Jessica
𝒎 = −𝟐𝒙 + 𝟒

39. Reflections

40. Reflections

41. Exit ticket
Complete the half page student survey and turn it in to me as you exit the room. (When the bell rings)
Keep your name card. You will use it again the next class period.