Question 20
Optical Illusion: Do you notice anything interesting about the following figure? How does this happen? Recreate this in your notebook.
- An optical illusion occurs when what we perceive visually differs from reality.
- In this figure (known as the Kanizsa Triangle), incomplete shapes trick our brain into filling in missing boundaries, creating the perception of a bright central triangle even though no triangle is actually drawn.
Step 1 · Identify the Illusion
A prominent white triangle appears in the center, seemingly resting on top of three black circles and an outlined triangle.
Although the edges of this white triangle appear sharp and clear, there are no actual lines drawn to form it.
Step 2 · Explain Why It Happens
The outer shapes are incomplete:
- Three black circles have wedge cutouts ("Pac-Man" shapes).
- Three "V" angles outline corners of a second triangle.
The brain naturally attempts to make sense of incomplete visual stimuli by filling in the gaps (forming illusory contours) to perceive a complete, familiar shape—in this case, an upright white triangle.
Step 3 · Recreate the Figure
To recreate this illusion in a notebook:
- Draw three filled black circles positioned at the vertices of an imaginary triangle.
- Cut a wedge out of each circle facing toward the center (like "Pac-Man" shapes).
- Draw three "V" angles between the circles pointing toward the center.
- Observe how an illusory white triangle immediately appears in the middle.
(i) We perceive a solid white triangle in the center that is not actually drawn. (ii) The brain automatically fills in the missing lines between the incomplete shapes to form a familiar pattern. (iii) Draw three inwardly-facing "Pac-Man" shapes and three "V" angles to recreate the illusion.
- Assuming Lines Exist: Mistaking the perceived white triangle for one with actual drawn boundaries, rather than recognizing it as an illusory contour generated by the brain.
- Incorrect Orientation When Drawing: Drawing the cutouts of the "Pac-Man" shapes facing away from the center, which breaks the illusion.
More questions in FIO
When constructing the perpendicular bisector, is it necessary to have the same radius for the arcs above and below ? Explore this through construction, and then justify your answer.
[Hint 1: Any point that is of the same distance from and 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 ? Instead, can we construct both the pairs of arcs on the same side of ? 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 in Fig. 6.4 is the perpendicular bisector.
Can you think of different methods to construct a 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 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 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 anywhere outside the line. Construct a perpendicular to the given line through .
[Hint: Find a line segment on whose perpendicular bisector passes through .]
How can the tangram pieces be rearranged to form each of the following figures?
Are the following tilings possible?