Elementary Math 2- Test 2

reflection symmetry def

easy to see, because one half is the reflection of the other half

line!

other names for reflection symmetry

mirror symmetry

line symmetry

the line of symmetry can...

be in any direction

how do you find if a shape has a line of symmetry- reflection symmetry test?

fold test

the number of reflection symmetries is the same as...

the number of sides in a regular (perfect) polygon

how many lines of symmetry does a circle have?

infinite- there are 360 degrees in a circle and each degree can be divided into infinitely many parts

how many lines of symmetry does a REGULAR 99-gon have?

99!

where is reflection symmetry most prevalent?

nature: leaves, flowers- daisy, grass

rotational symmetry def

a shape has rotational symmetry when it still looks the same after a rotation

turn

what is order?

how many times it matches when we go around

number of rotations that look alike

do humans have rotational symmetry?

yes! every item has rotational symmetry

think of doing a cartwheel

where can rotational symmetry be seen?

blade of grass- nature, ceiling fan

is there rotational symmetry of order 1?

yes but no, it's only counted if there are others. If there are not any others, than it is trivial

point symmetry def

it looks the same upside down as right side up

properties of point symmetry

the same distance from the central point

but in the opposite direction

has to have at least rotational order of 2

if a shape doesn't have rotational symmetry...

it doesn't have point symmetry

what is another name for point symmetry? why?

origin symmetry because origin is the central point about which the shape is symmetrical

you can have rotational without point...

but you can't have point without rotational

examples of point symmetry

deck of cards

eraser

shape of a book

if a shape is regular...

it will have the same number rotation and reflection symmetries

tessellations

a repeating pattern of shapes that covers a space that fit together without gaps or overlaps

where does the word tessellation come from?

from a latin word meaning tile

earliest tessellations

islamic art from around 3,000 BC

M.C. Escher is the father of modern tessellations

where can a tessellation be found?

nature- dragonfly wings, honeycomb, pineapple skins, etc.

art

architecture

computer science

mapping

What must a tessellation have?

the shapes must fit together without any gaps

the shapes should not overlap

naming a tessellation

go around a vertex and write down how many sides each polygon has, in order from smallest to largest

demiregular tessellation

also called other

mathematicians disagree on what they actually are

how many demiregular tessellations are there

infinitely many

semi-regular tessellation

made up of two or more regular polygons. the pattern at each vertex must be the same.

how many semi-regular tessellations are there?

8

regular tessellation

pattern made by repeating a regular polygon (equilateral triangle, square, regular hexagon)

rules for REGULAR tessellations

tessellation must tile a floor that goes on forever with no overlapping or gaps

the tiles must be regular polygons- and they must al be the same

each vertex must look the same

why will a pentagon not tessellate?

(n-2) 180= (5-2) 180= (3) 180= 540

540/5= each angle is 108 degrees

108 + 108 + 108= 324 degrees- won't tessellate because there will be gaps because it's less than 260 degrees

what is a vertex

corner point

how to know if a shape will tessellate

if the sum of the angles around the vertex are less than 360- there will be gaps

if the sum of the angles around the vertex are greater than 360- there will be overlaps

what is point symmetry a subset of

rotational

how many reflection symmetries or lines of symmetries can a triangle have?

3- equilateral

1- isosceles

none- scalene