Nature and Patterns in Mathematics - Flashcards

Flashcards covering symmetry, types of symmetry, rotational and translational concepts, spirals, tessellations, fractals, and basic number patterns with arithmetic sequences.

What is symmetry in mathematics?

A rigid motion of the plane that leaves the object unchanged.

What does the Greek word symmetria mean?

The same measure.

What is reflectional (mirror) symmetry?

Bilateral symmetry with a line or axis of symmetry.

How many axes of symmetry does this flower have?

Four axes of symmetry.

How many axes of symmetry does a five-armed starfish have?

Five axes of symmetry.

What is rotational symmetry?

A rigid motion about a fixed center that makes the object look the same after rotation.

What is the center in rotational symmetry?

The fixed point about which the rotation occurs.

What does 'order' mean in rotational symmetry?

The number of times an object can be rotated by an angle less than 360° to look the same.

What is the angle of rotation in rotational symmetry?

The number of degrees through which the object is rotated to look the same.

What is translation symmetry?

A pattern has translation symmetry if a part has been moved the same distance in the same direction, preserving orientation.

Does translation change an arrow pattern after several movements?

No; translation preserves orientation and the pattern remains unchanged.

What property leads to spirals in patterns?

Self-similarity or scaling; the same shape is maintained as the object grows.

What is tessellation (tiling)?

A pattern made of one or more geometric shapes joined without overlaps or gaps to cover a plane.

Where can tessellations be observed in nature?

In natural tiling patterns where shapes fit together without gaps.

What is a fractal?

Never ending replication of a pattern at different scales; self-similarity.

What is a number pattern?

A pattern or sequence of numbers arranged in a specific order that follows a rule.

What is the rule for the sequence 1, 2, 3, 4, 5, …?

Add 1 to the previous term.

What is the rule for the sequence 2, 4, 6, 8, 10, …?

Add 2 to the previous term.

What is the formula for the nth term of an arithmetic sequence?

an = a1 + (n − 1) d.

What is the common difference for the sequence 3, 8, 13, 18, 23, …?

5.

What is a_50 for the sequence 3, 8, 13, 18, 23, …?

248.

What is the general nth-term formula for the sequence 3, 8, 13, 18, 23, …?

a_n = 3 + (n − 1)·5.

What is the 35th term of the sequence 18, 15, 12, 9, …?

-84.

What does the sequence 1, 4, 9, 16, 25 represent in terms of n?

a_n = n^2 (the square of the position).

Is the sequence 3, 10, 17, 24, … an arithmetic sequence? If so, what is the common difference?

Yes; the common difference is 7.