MSE2183
Assignment 2
Unique No: 808426
Due 7 July 2025
,MSE2183
Assignment 2
Unique Number: 808426
Due Date: 07 July 2025
Geometry in Nature, Manipulatives, Software, and Pedagogical Theories
Question 2: Geometry in Nature and Building Blocks of Geometry
2.1 Geometry in Nature
2.1.1 Three Natural Objects with Geometric Shapes
Objective: Identify three natural objects with geometric shapes, name their shapes, and
describe them with sketches.
Snowflakes
• Shape: Hexagonal symmetry (six-fold rotational).
• Description: Snowflakes exhibit hexagonal patterns due to water molecule
arrangement under specific conditions, reflecting Euclidean symmetry and fractal
self-similarity (Wilson, 2017).
• Sketch: Draw a six-pointed star with a central hexagon, each arm branching into
smaller hexagons, labeled to show rotational symmetry.
, Analysis: The hexagonal structure optimizes molecular packing, illustrating
geometry's role in natural efficiency (Ball, 2016).
Nautilus Shell
• Shape: Logarithmic spiral.
• Description: The shell’s spiral follows the golden ratio, with radius increasing
logarithmically, representing a non-Euclidean form tied to growth patterns
(Dunlap, 2004).
• Sketch: Draw a spiral from a central point, with compartments expanding
proportionally, labeled to indicate logarithmic growth.
•
Analysis: The spiral challenges Euclidean simplicity, highlighting non-Euclidean
applications in nature.
Assignment 2
Unique No: 808426
Due 7 July 2025
,MSE2183
Assignment 2
Unique Number: 808426
Due Date: 07 July 2025
Geometry in Nature, Manipulatives, Software, and Pedagogical Theories
Question 2: Geometry in Nature and Building Blocks of Geometry
2.1 Geometry in Nature
2.1.1 Three Natural Objects with Geometric Shapes
Objective: Identify three natural objects with geometric shapes, name their shapes, and
describe them with sketches.
Snowflakes
• Shape: Hexagonal symmetry (six-fold rotational).
• Description: Snowflakes exhibit hexagonal patterns due to water molecule
arrangement under specific conditions, reflecting Euclidean symmetry and fractal
self-similarity (Wilson, 2017).
• Sketch: Draw a six-pointed star with a central hexagon, each arm branching into
smaller hexagons, labeled to show rotational symmetry.
, Analysis: The hexagonal structure optimizes molecular packing, illustrating
geometry's role in natural efficiency (Ball, 2016).
Nautilus Shell
• Shape: Logarithmic spiral.
• Description: The shell’s spiral follows the golden ratio, with radius increasing
logarithmically, representing a non-Euclidean form tied to growth patterns
(Dunlap, 2004).
• Sketch: Draw a spiral from a central point, with compartments expanding
proportionally, labeled to indicate logarithmic growth.
•
Analysis: The spiral challenges Euclidean simplicity, highlighting non-Euclidean
applications in nature.
