When someone asks if a polygon can tesselate a plane,what exactly are they asking?

Question

1)When someone asks if a polygon can tesselate a plane,what exactly are they thinking? Explain yourself thoughtfully and carefully. 2)How someone can figure out whether a figure will or will not tesselate(tile) a plane without actually trying it?

Answer 1

The only regular polygons(all sides congruent and all angles congruent) that can tesselate a plane(because of the reasons stated above) are:

Equiliateral triangle: Int. angles 60 degrees. 6 at each vertex
Square. Int. angles 90 degrees, 4 at each vertex.
Hexagon: Int. angles 72 degrees, 5 at each vertex.

These are the only regular polygons that you could tile a floor with having no gaps at the vertex. There are an infinite number of non-regular polygons that will tesselate the plane, such as any rectangle or triangle, and others. Have fun!

Answer 2

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RE:
When someone asks if a polygon can tesselate a plane,what exactly are they asking?
1)When someone asks if a polygon can tesselate a plane,what exactly are they thinking? Explain yourself thoughtfully and carefully. 2)How someone can figure out whether a figure will or will not tesselate(tile) a plane without actually trying it?

Answer 3

You form a mosaic on a plane with polygons, such as triangles. It has been a while for me, but, two triangles make a diamond, six triangles make a hexagon and so on. Other polygons can be used this way. Put " tessellate " into your address bar, or goggle it. PS to know if things tessellate, you would know there area. A=1/2bh

Answer 4

Define

tessellate
The repeated use of geometric figures to completely cover a plane without overlapping.

2)How someone can figure out whether a figure will or will not tesselate(tile) a plane without actually trying it?

The key features of tessellations are that there are no gaps or overlaps. The same figure (or group of figures) come together to completely cover a wall or floor or some other plane. This requires the vertices to fit together. This can be done in two ways. Either the corners of the basic shape all fit together to make 360° , or the corners of some basic shapes fit together along the side of another to again make 360° .
http://www.nzmaths.co.nz/geometry/symmetry/KeepInShape.aspx

http://www.bagatrix.com/glossary/math_glossary_t.htm

Tessellation Tutorials
http://mathforum.org/sum95/suzanne/tess.intro.html

Tessellation
http://mathworld.wolfram.com/Tessellation.html

Tessellation Links
http://mathforum.org/sum95/suzanne/links.html

Answer 5

Hi. If the polygon can fit together in a repeating pattern then tesselation is a given. : http://www.answers.com/main/ntquery?s=tesselate&gwp=16

Answer 6

Squares tesselate because if you put them next to each other there are no gaps in between. The only way to know is to try it (Even if you just draw some figures quickly) or be able to picture it in your head. I think octagons tesselate too.

Answer 7

Just adding to the first answer, regular octagons do not tessellate a plane. However, regular hexagons, equilateral triangles, and squares would. Good night!

Answer 8

They are asking if you could tile an area with this polygon without any gaps and without any other polygon to help cover any gaps.

The polygon in its original state must have angle measures that can evenly divide into 360 degrees.

I hope this helps.