Mathematics in natureSunna Austmann Bjarnadóttir

and

Þórhildur Grímsdóttir

Transformation

Reflection, translation and rotation are all types

of transformation

Definition: Transformation of the Plane

Definition: Rigid Motion of the Plane

Transformation

Four transformations of the plane have special importance. They are the four rigid motions of the plane: translations, rotations, reflections and glide-reflections. We will talk about the first three.

Definition for the Transformation of the Plane is a one-to-one correspondence of the set of points in the plane to itself is a transformation of the plane. If point P corresponds to point P1, then P1

is called the images of P under the transformation. Point P is called the preimage of P1.

Definition for the rigid motion of the plane is a transformation of the plane is a rigid motion if, and only if, the distance between any two points P and Q equals the distance between their image points P1 and Q1. That is, PQ=P1 Q1 for all points P and Q.

Reflection

Reflection

Reflection is also called a flip or a mirror

reflection.

Reflection is an exact copy of the original image

When working with this type of transformation in

the coordinate system the image is flipped over

the reflection axes by means of coordinates.

Reflection

Refletion in water Reflection in leaves

Translation

Translation

Translation, also known as a slide, is the rigid

motion in which all points are moved the same

distance in the same direction.

Translation

Translation in a fish skin Translation in a vasp‘s

body

Rotation

Rotation

A rotation, also called turn, is the movement

where the image is rotated about a center-point

through the same number of degrees - the turn

angle or angle of rotation.

It is turned counter clockwise.

Rotation

Rotation in flowers petals

and

in a weather picture

Pattern

Translation

symmetry

Rotation

symmetry

Reflection

symmetry

Pattern

Pattern is usually made up of a certain pattern

unit that is repeated over and over again,

regularly or irregularly.

Patterns can be both two dimensional and three-

dimensional.

Pattern

Dilation Similarity motions

Pattern

Dilation, also called size transformation, is the

simplest transformation to change the size of a

figure, but it preserves its shape and orientation.

Patterns can be found all around you, including

in animal fur, fabric and art.

Polygons - Polyhedrons

Polygons - Polyhedrons

Polygons are to be found all a round us.

They are only outlines of a subject such as triangels, squares and other quadrilaterals, pentagons, hedragons and circles.

A plane of a polygon has an area and they are two dimensional.

Polyhedrons are three dimensional such as all kind of prisms, cylinders, cones and pyramids.

They are made up from polygons and their surface area and volume can be measured.

Polygons - Polyhedrons

Pines shapesMountain Keilir

Cone - keila

Thank you!

„Maths is everywhere“

Comenius project

October 2012

Bibliography

http://sisimiutlv.blogcentral.is/AlbumImage.ashx?id=1802969

http://www.hort.purdue.edu/ext/senior/vegetabl/images/large/beanleaves56.jpg

http://fashionfiles.typepad.com/.a/6a011168fc0651970c0120a60e55e4970c-800wi

http://www.pestcontrolservicemelbourne.com.au/wp-content/uploads/2010/04/wasps-melbourne.jpg

http://visindavefur.hi.is/myndir/laegdirisl_220611.jpg

http://www.flickr.com/photos/aammiirr/4527931702/

http://vefir.unak.is/heimaslod/grennd/blominbig.jpg

http://www.kommunan.is/sverrir/wp-content/gallery/dyr/lundi-web.jpg

http://thumbs.dreamstime.com/thumblarge_492/127025355381fjbt.jpg

http://www.skuggar.blog.is/users/cb/skuggar/img/_smsfs1cluster_shl_hjorturb_my_documents_keilir.jpg