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Sirje Sild

on 31 October 2014

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Transcript of Tessellation

We have all played with puzzles trying to cover the surface without the gaps between nor overlapping the pieces. Creating a tessellation means covering a flat surface with shapes with no overlaps and no gaps between the shapes.
Notice Mathemayics around You
The 7th competition for pupils named Notice Mathematics around You was held in Estonia on the school year 2013/2014. This time the task was to create a tessellation. We received 250 works from pupils in grades 7 to 12.
What is tessellation?
I place
Mari Mikson, Paide Gümnaasium
Teacher: Daire Krabi

Head of a horse made for the Horse Year.
To create the head of the horse, two polylines had to be used.
Translating by vector until the tessellation is created.
I will show you the best works done
by pupils and lets try to figure
out how these have been made.
The pupils are very inventive and
made very nice worksheets.


Nõo Science School is one of the five general education state schools of the Republic of Estonia. (i.e. educational, dormitory, and transport expenses are covered by the state.)
The vision of Nõo Science School is to be a highly appreciated secondary school in Estonia with intensive teaching in science, being innovative and promotive of knowledge and technologies.
Our mission is to be realistic in our acts, flexible in solutions, optimistic in chances, and open for wide cooperation.

Nõo Science School
In the autumn of 1965, the computing centre was built next to Nõo Secondary School. The University of Tartu gave the school an electronic computer „Ural-1“, making the computing centre of Nõo Secondary School the very first one in the whole Soviet Union to be used by a general educational school.
The graduates of Nõo School can get a technician-programmer vocation in case they perform a specific exam.
Sirje Sild
Nõo Science School

Large amount of work done. There are more than 4000 lines in the construction protocol. Estonian national flower, blue cornflower is made by using the tessellation. The cornflower is made by using the regular hexagon. The barn swallow is not created by using tessellation.
I place
Diana Belolipetskaja
Tartu Annelinna Gümnaasium
Teacher: Maksim Ivanov

Grades 10-12
You get the instruction guide from me which is the same what pupils were given

II place
Janely Vestli, Virtsu Kool
Teacher: Siivi Jõgi

1. Created a triangle.
2. Created the polyline on one side.
3. Rotated the polyline 60 degrees around the vertex.
4. Found the midpoint of the 3rd side of the triangle and drew a polyline from
the vertex to the midpoint.
5. Rotated the polyline 180 degrees
around the midpoint.
You can draw the shape yourself. To get the symmetry you have to reflect the object in a line. To cover the surface, translate the shape by a vector
Diana started the work by drawing the spider on a squared paper.
To create the tessellation the teacher made a command (using lists and translating by vector).

III place
Pjotr Volostnõh, Tallinna Läänemere Gümnaasium Teacher: Marina Mets
Draw a circle p with the
midpoint A and radius 4.
Point B.Rotate[Point[Circle[A, 3]], α]
Reflect point B in point A. Point B’ is created.
Point L.Rotate [Point[p], α - 30° + β]
II place
Kert Kaasik, Madis Janno; Paide Ühisgümnaasium*
Teacher: Margit Arro

Translating by vector to get the copy of the polyline.
The polygon depicting the
head of the horse was created
by using a photo.The head shaped
polygon was first added to the
The advanced object properties were used
to add polygons to different layers

The authors of the best works have used the guide, but also used other options in GeoGebra. There are lots of different tools that can be used to make a unique work.
Many nice tessellatsions!
Grades 7-9
III place
Angelina Šumilova, Kohtla-Järve Järve Gümnaasium
Teacher: Maarika Virkunen
Full transcript