Question 4 - Figure it out - Page 100, 101 - Chapter 4 Class 8 - Exploring Some Geometric Themes (Ganita Prakash II

Transcript

Question 4 Observe this triangle. (i) Would it be possible to build a model out of actual cubes? What are the front, top, and side profiles of this impossible triangle?This is called a Penrose Triangle Here is its animation No, it is not possible to build this as a single, solid, closed triangle in 3D space. Reason: If you start at one corner and follow the cubes, you are moving in three different directions (Height, Length, and Depth). To close the triangle, the last cube would have to be in two places at once. The "Trick" Exception: You can build a "forced perspective" model. This is a model where the bars don't actually touch (there is a big gap), but if you close one eye and stand at a very specific spot, the bars line up to look like they touch. Here is Teachoo’s attempt Question 4 Observe this triangle. (ii) Recreate this on an isometric grid.It would look like this Question 4 Observe this triangle. (iii) Why does the illusion work?The illusion works because of two things: 1. Isometric Limitation: In isometric drawing, there is no perspective. In real life, things further away look smaller. In isometric, they stay the same size. This "cheats" your eye into thinking a bar that is far away is actually right next to a bar in the front. 2. Brain Logic: Our brains are "hard-wired" to see 3D shapes. When we see three lines meeting at a point on a grid, our brain automatically assumes it’s a solid corner. The drawing uses these "corners" to lead your eye in a circle that contradicts itself.