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These flashcards review the lecture’s central ideas: the nature of mathematics, common natural patterns and their properties, Fibonacci sequence basics, and the precision of mathematical language.
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What are the two main cognitive abilities required in mathematics?
Logical thinking/problem-solving and creative/abstract thinking.
Complete the quote: “Mathematics is the __ with which God has written the universe.”
language
Define a pattern in the context of nature.
A visible, regular form or sequence found in the natural world that can often be modeled mathematically.
What special line divides an object into two identical halves in bilateral symmetry?
Line of symmetry (mirror line).
Give an example of bilateral symmetry in living things.
Human body, orchid flower, or a leaf with two identical halves.
How is radial symmetry different from bilateral symmetry?
Radial symmetry has more than two identical parts arranged around a central point, whereas bilateral symmetry has two mirrored halves.
Explain cyclic symmetry and give one example.
Symmetry with rotation only; rotating the figure about the center leaves it unchanged. Example: a 5-armed starfish (C₅ symmetry).
Explain dihedral symmetry and give one example.
Symmetry that combines rotation and reflection; the object can be rotated and reflected across mirror lines. Example: a snowflake (D₆ symmetry).
What is the defining property of a fractal?
Self-similarity—the same shape repeats at different scales.
Why are natural fractals considered only approximate?
Infinite iteration is impossible in nature, so real-world fractal patterns terminate after several levels.
Describe a spiral in mathematical terms.
A curve that emanates from a point and moves farther away as it revolves around that point.
How is the Fibonacci sequence generated?
Each term after the second is the sum of the two preceding terms.
Write the next two terms of the Fibonacci sequence 1, 1, 2, 3, 5, 8, __, __.
13, 21
What is tessellation?
A pattern formed by repeating tiles that cover a flat surface without gaps or overlaps.
Why do soap bubbles form spheres?
A sphere has the minimal surface area for a given volume, minimizing surface tension.
What adaptive advantage do animal stripe patterns often provide?
Camouflage or signaling that increases offspring survival and reproduction chances.
What information can crack patterns reveal about a material?
Whether the material is elastic or not, based on how it relieves stress.
State three characteristics of mathematical language.
Precise, concise, powerful.
In mathematical language, what corresponds to an English noun?
A mathematical expression (it names a quantity or object but does not make a complete statement).
What is the mathematical analogue of an English sentence?
A mathematical sentence (an equation or inequality that states a complete thought).