MMW L1

What does the Greek word “Mathema” mean?

That which is learnt

“lesson.”

A science of patterns.

What is mathematics described as?

Pythagoras

 A mathematician known as the Father of Numbers who discovered numerical reasons in musical harmony.

logic patterns

Patterns that deal with the characteristics of objects and their order

aptitude tests

Where are logic patterns commonly used?

 Find the rule, understand the sequence, and analyze the difference between the numbers or objects

What should you do to solve or construct a pattern?

 Mathematics uses them to make predictions, and they lead directly to the concept of functions.

Why are number patterns useful?

11, 13, 17, 19, 23, ___

What is an example of a number pattern in the lesson?

 5, 7, 10, 15, 22, ___

What is an example of a number pattern in the lesson?

25

•What is the next number in the sequence: 11, 13, 17, 19, 23, ___?

29

•What is the next number in the pattern: 5, 7, 10, 15, 22, ___?

Patterns in Nature

Regularities in different forms that occur naturally in the natural world.

fractal

 A detailed pattern that looks similar at any scale and becomes more complex when observed at larger scales.

spiral

A curved pattern that focuses on a center point with circular shapes revolving around it.

Voronoi

A pattern that provides clues about nature's tendency toward efficiency, such as the nearest neighbor, shortest path, and tightest fit.

tessellation

 A design or pattern where a shape is repeatedly used to cover a plane with no gaps, overlaps, or empty spaces.

regular tessellation

A tessellation made using only one type of regular polygon.

What is a semi-regular tessellation?

A tessellation where the same combination of regular polygons meets at each vertex.

What is an irregular tessellation?

A tessellation using irregular polygons, which may be the same or different types.

Reflection, rotation, and translation

What are the three transformations mentioned for extending a basic design?

 transformation

A process that changes a figure into another figure. The new figure is called the image.

reflection

 A transformation that flips a figure across a line called the line of reflection

Symmetry

Different sides of something that are like, it creates a mirror image

reflectional symmetry

When a shape can be folded in half and both sides match exactly.

rotation

A transformation that turns a figure around a point or line. Turning the figure about a given point creates a center of rotation

rotational symmetry

When a shape can be rotated less than one full turn and still look the same as the original.

translation

A transformation where a figure slides without turning, while keeping its size and shape.

They move the same distance and in the same direction.

What happens to all points during translation?

dilation

A transformation that makes a figure larger or smaller with respect to a center of dilation.

scale factor

The ratio of the side lengths of the image to the corresponding side lengths of the original figure.

Leonardo of Pisa, a 13th-century Italian mathematician known as Fibonacci.

Who is the Fibonacci sequence named after?

By adding the previous two numbers together.

How is each number in the Fibonacci sequence created?

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

Give an example of the Fibonacci sequence.

34 and 55

2 numbers in fibonacci sequence

Golden Ratio

A special number obtained when a line is divided into two parts so that the longer part divided by the smaller part equals the whole length divided by the longer part.

φ ≈ 1.618.

What is the approximate value of the Golden Ratio?