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Questions and Answers
What is the approximate percentage of the total area made up by the circles in the packing problem?
What is the approximate percentage of the total area made up by the circles in the packing problem?
Which geometric shape has its total area represented as approximately90% in the packing problem?
Which geometric shape has its total area represented as approximately90% in the packing problem?
What does symmetry in nature indicate?
What does symmetry in nature indicate?
Which type of symmetry is exhibited by Leonardo da Vinci’s Vitruvian Man?
Which type of symmetry is exhibited by Leonardo da Vinci’s Vitruvian Man?
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What is the definition of a pattern as per the text provided?
What is the definition of a pattern as per the text provided?
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What does identifying patterns in nature help individuals do?
What does identifying patterns in nature help individuals do?
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Which of the following terms is used to describe when you can draw an imaginary line across an object and have mirror images?
Which of the following terms is used to describe when you can draw an imaginary line across an object and have mirror images?
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In what way does rotational symmetry differ from bilateral symmetry?
In what way does rotational symmetry differ from bilateral symmetry?
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What is the smallest measure of angle that a figure can be rotated while still preserving the original position called?
What is the smallest measure of angle that a figure can be rotated while still preserving the original position called?
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If a figure has a rotational symmetry of order 6, what is the angle of rotation?
If a figure has a rotational symmetry of order 6, what is the angle of rotation?
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Why do bees use hexagons in making honeycombs?
Why do bees use hexagons in making honeycombs?
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What is the packing problem referring to?
What is the packing problem referring to?
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What is the order of rotational symmetry for a snowflake pattern that repeats six times?
What is the order of rotational symmetry for a snowflake pattern that repeats six times?
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Study Notes
Patterns in Nature
- A pattern is a regular, repeated, or recurring form or design.
- Examples of patterns in nature include:
- Butterfly's bilateral symmetry
- Leonardo da Vinci's Vitruvian Man's proportion and symmetry
- Starfish's rotational symmetry
Symmetry
- Symmetry indicates that an object can be divided into two identical parts, like a mirror image.
- Types of symmetry include:
- Bilateral symmetry (left and right sides are identical)
- Rotational symmetry (object remains unchanged after rotation)
- Examples of symmetry include:
- Butterfly's bilateral symmetry
- Starfish's rotational symmetry
Packing Problem
- The packing problem involves finding the optimal method of filling a given space with shapes.
- Calculations for packing problem:
- Area of a circle: 𝜋𝑐𝑚2
- Area of a square: 𝑠𝑖𝑑𝑒2 ∙ 3/4
- Area of a hexagon: 6 × 3 𝑐𝑚2
- Efficiency of packing shapes:
- Square packing: ≈ 78.54% efficient
- Hexagonal packing: ≈ 90.69% efficient
Rotational Symmetry
- Rotational symmetry occurs when an object remains unchanged after rotation by a certain angle.
- Order of rotation (n) is the number of times an object can be rotated by a certain angle and still appear unchanged.
- Formula for angle of rotation: 𝐴𝑛𝑔𝑙𝑒 𝑜𝑓 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 = 360° / 𝑛
- Example: The snowflake has a 6-fold rotational symmetry, with an angle of rotation of 60°.
Honeycomb
- Honeycomb's hexagonal structure is an efficient way to pack shapes.
- Bees use hexagons to make honeycomb because it allows for maximum storage and minimum use of wax.
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Description
Enhance your ability to identify patterns in nature and regularities in the world with Mr. Augustus Ceazar L. Lodronio, LPT. Delve into the significance of Mathematics in everyday life and appreciate the concept of patterns, regularity, and relationships in nature.
