Question 20
Optical Illusion: Do you notice anything interesting about the following figure? How does this happen? Recreate this in your notebook.
Our brain creates a shape that is not really there.
Step 1 — What we see
Look closely at the figure. We see a white triangle in the middle. It looks like it is on top of other shapes. The edges of this white triangle are very clear. But if we trace the lines, there is no triangle drawn.
Step 2 — How this happens
The shapes around the center are incomplete. There are three black "Pac-Man" shapes. There are also three "V" shapes. Our brain tries to make sense of these parts. It fills in the missing information. It creates the perception of a white triangle. This is an optical illusion. It shows how our brain actively constructs what we see.
Step 3 — Recreating the illusion
Take out your notebook. Draw three black circles. Cut a wedge out of each circle. These are like "Pac-Man" shapes. Place them at the corners of a triangle. Make sure their "mouths" point inwards. Now draw three "V" shapes. Place them between the "Pac-Man" shapes. Make sure their open ends also point inwards. You will see a white triangle appear. This triangle is not actually drawn.
Answer
(i) We notice a white triangle in the center. It appears to be on top of the other shapes. (ii) This happens because our brain tries to complete the incomplete shapes. It fills in the missing lines to create a familiar shape, the triangle. This is called an optical illusion. (iii) To recreate it, draw three "Pac-Man" shapes and three "V" shapes. Arrange them so their open parts point towards the center of an imaginary triangle. Your brain will then perceive a white triangle.
More questions in FIO
When constructing the perpendicular bisector, is it necessary to have the same radius for the arcs above and below XY? Explore this through construction, and then justify your answer.
[Hint 1: Any point that is of the same distance from X and Y lies on the perpendicular bisector.
Hint 2: We can draw the whole line if any two of its points are known.]
Is it necessary to construct the pairs of arcs above and below XY? Instead, can we construct both the pairs of arcs on the same side of XY? Explore this through construction, and then justify your answer.
While constructing one pair of intersecting arcs, is it necessary that we use the same radii for both of them ? Explore this through construction, and then justify your answer.
Recreate this design using only a ruler and compass —
Justify why AB in Fig. 6.4 is the perpendicular bisector.
Can you think of different methods to construct a 90° angle at a given point on a line using a rope?
Construct at least 4 different angles. Draw their bisectors.
Construct the 8-petalled figure shown in Fig. 6.5.
In Step 2 of angle bisection, if arcs of equal radius are drawn on the other side, as shown in the figure, will the line OC still be an angle bisector? Explore this through construction, and then justify your answer.
What are the other angles that can be constructed using angle bisection? Can you construct 65.5° angle?
Come up with a method to construct the angle bisector using a rope.
Construct the following figure.
How do we construct the petals so that they are of the maximum possible size within a given square?
Construct at least 4 different angles in different orientations without taking any measurement. Make a copy of all these angles.
Construct the Fig. 6.6.
Construct 4 pairs of parallel lines in different orientations.
Construct the following figure.
Use support lines in Fig. 6.11 to construct a pointed arch. Make different arches, by changing the radius of the arcs.
Make your own arch designs.
Construct the following figures:
Optical Illusion: Do you notice anything interesting about the following figure? How does this happen? Recreate this in your notebook.
Construct this figure.
[Hint: Find the angles in this figure.]
Draw a line and mark a point P anywhere outside the line. Construct a perpendicular to the given line through P.
[Hint: Find a line segment on whose perpendicular bisector passes through P.]
How can the tangram pieces be rearranged to form each of the following figures?
Are the following tilings possible?