Fractals and Visualising Solids | A

Question 1

Build it in Your Imagination

We will start this section by practising visualisation. For each prompt, feel free to talk to your partner, gesture, draw it in the air — but do not actually draw on paper!

  1. Picture your name, then read off the letters backwards. Make sure to do this by sight, not by sound — really see your name! Now try with your friend's name.
Check your answer with HomiSolve it yourself, then let Homi check your steps and spot mistakes.
Solution
Understand the Question
  • Visualisation is the ability to form clear mental images of objects, shapes, or words without drawing them on paper.
  • The goal is to hold a word in your visual memory and scan it from right to left using your "mind's eye" (by sight) rather than sounding it out (by phonetics).

Step 1 · Visualise and Read Your Name Backwards

Imagine a name, for example JOHN, clearly displayed in your mind.Diagram 1

Now, scan the letters in your mind from right to left:

  • The last letter is N
  • The previous letter is H
  • The next letter is O
  • The first letter is JDiagram 2

Therefore, JOHN read backwards by sight is NHOJ.

Step 2 · Visualise and Read a Friend's Name Backwards

Now imagine a friend's name, for example MARY, in your mind: M, A, R, Y.Diagram 3

Scanning the letters visually from right to left:

  • The last letter is Y
  • The previous letter is R
  • The next letter is A
  • The first letter is M

Therefore, MARY read backwards by sight is YRAM.

Answer

(Answers may vary depending on the names chosen)

  • Your Name (e.g., JOHN): NHOJ\text{NHOJ}
  • Friend's Name (e.g., MARY): YRAM\text{YRAM}
Common Mistakes
  • Relying on Sound instead of Sight: Trying to phonetically pronounce the word backwards rather than scanning the actual visual shapes of the letters from right to left.
  • Reversing Individual Letter Glyphs: Confusing reversing the order of letters (e.g., JOHNNHOJ\text{JOHN} \rightarrow \text{NHOJ}) with mirror-flipping individual letter shapes.

More questions in A

Q1

Build it in Your Imagination

We will start this section by practising visualisation. For each prompt, feel free to talk to your partner, gesture, draw it in the air — but do not actually draw on paper!

  1. Picture your name, then read off the letters backwards. Make sure to do this by sight, not by sound — really see your name! Now try with your friend's name.
Q2

Cut off the four corners of an imaginary square, with each cut going between midpoints of adjacent edges. What shape is left over? How can you reassemble the four corners to make another square?

Q3

Mark the sides of an equilateral triangle into thirds. Cut off each corner of the triangle, as far as the marks. What shape do you get?

Q4

Mark the sides of a square into thirds and cut off each of its corners as far as the marks. What shape is left?

Q5

Net of a sphere? Experiment and see if you can make a paper cutout that can perfectly wrap around a ball without leaving any wrinkles, gaps or overlaps.

Q6

Place an object in front of a plane, such as a wall of your room. Shine a torch light on the object in a direction perpendicular to the wall.

What do you see?

Q7

Observe what happens to the size of the shadow as you vary the distance between your torch and your object.

Q8

Context: Observe what happens to the size of the shadow as you vary the distance between your torch and your object.

Q. Why does this happen?

Q9

Construct a model of a cube and use your hands to keep it balanced on one corner vertex. Can you try to understand why all the projected edges have equal length?

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