Batch 3 - Class 154 - Dimensions and Perspective
Preclass Exercise:
- Is the surface of earth 2-dimensional or 3-dimensional?
- What is dimension?
- It is 2-dimensional, since all points on the surface can be expressed using two independent values (eg: latitude and longitude). It is, however, embedded in a 3-D space
Attendance Arjun, Muskaan, Anshi, Veer, Manya
Class puzzles
- What will the following shapes fold up to?
- Answer: Prism and pyramid (tetrahedron)
Using Perspectives
- Explain the notion of perspectives to kids, by taking a 3D object and drawing its three perspectives.
- Find all possible cubical buildings that have a base, and front projection and a right side projection that is as follows
.png)
- Answer: 7 solutions. 2 with 6 cubes, 4 with 7 cubes, 1 with 8 cubes
- Is there number of cubes determined by the following perspectives
.png)
- Answer: Yes
- Is there number of cubes determined by the following perspectives
.png)
- Answer: Yes
.png)
- Use exactly 20 cubes to make a model from the building plans below. Record the base plan for your building. What are the maximum and minimum numbers of cubes that could be used to build the structure.
.png)
- Answer: The range of number of cubes is 18-22. 20 cube answer is as under (there are several answers)
.png)
- (MartinShCol - 6.8) Design a cork so that it fits a square, a circular and a triangular hole snugly.
- Answer: Take a cylindrical cork standing on a face, and cut a triangle as you look at it. The base provides the circular fit, the cylinder's cross section provides square, and the triangle is the third.
.png)
Stadium Seating
You want to design stadium seating so that every spectator can see the stadium. This of course requires the seats at the back to be higher than the seats in front. In this particular stadium, every spectator should be able to see a point 10m in front of the first seat. The other parameters are shown below - essentially every person should get a 0.2m clearance over the person in front.
- How high above the ground does the second row seating needs to be?
- How high above the ground does the third row seating needs to be?
- If there were 40 rows, how high does each row need to be? Can you plot the same? Do the seats need to curve up or down?
- In reality, the 0.2 clearance doesn't need to be uniform - it needs to be the highest on bottom rows (higher sensitivity due to flatter view), and can be lower later. Also, stadia are usually built as concourses, so that the effect of vertigo is not high. See below:
Homework Problem:
- Arrange six people in a pattern so that each of them can see exactly 4 other people. Note that a person in middle can block the view for what is beyond them.
- Answer:
.png)
References:
The Colossal Book of Short Puzzles and Problems, by Martin Gardner