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What best describes a semi-regular tessalation?
A semi-regular tessellation consists of two or more types of regular polygons that are arranged in a repeating pattern to fill a plane without any gaps or overlaps. Each vertex in a semi-regular tessellation has the same arrangement of polygons around it, maintaining a consistent geometric structure. Examples include the patterns formed by squares and equilateral triangles or hexagons. These tessellations create visually appealing designs while adhering to mathematical principles.
What regular polygons fit around a vertex point?
Regular polygons that can fit around a vertex point must have interior angles that add up to 360 degrees when placed around that point. The regular polygons that meet this criterion are the triangle (60 degrees), square (90 degrees), pentagon (108 degrees), hexagon (120 degrees), and dodecagon (30 degrees). Other polygons with larger numbers of sides can also fit, provided their interior angles are divisors of 360 degrees. Thus, any regular polygon with an angle that divides 360 degrees can fit around a vertex point.
What following polygons can form a regular tessellation?
Regular tessellations can be formed by three types of polygons: equilateral triangles, squares, and regular hexagons. These shapes can cover a plane without gaps or overlaps, as their internal angles appropriately fit together. Other polygons, such as pentagons or heptagons, do not create a regular tessellation because their angles do not allow for a perfect fit around a point.
Will a regular polygon tile?
There are only three regular polygons which with tile. These a re a triangle, quadrilateral (square) and hexagon.This is because if there are n tiles meeting at a point, then the sum of the angles around that point must be 360 degrees - otherwise the polygons will overlap. The only regular polygons with interior angles that are factors of 360 are the ones mentioned above.
In a tessellation the angles of the regular polygons around a given vertex what do they always add up to?
They add to 360 degrees.
What best describes a semi-regular tessalation?
A semi-regular tessellation consists of two or more types of regular polygons that are arranged in a repeating pattern to fill a plane without any gaps or overlaps. Each vertex in a semi-regular tessellation has the same arrangement of polygons around it, maintaining a consistent geometric structure. Examples include the patterns formed by squares and equilateral triangles or hexagons. These tessellations create visually appealing designs while adhering to mathematical principles.
What is the angle sum around a vertex in a tessellation?
In a tessellation, the angle sum around a vertex depends on the type of polygons used in the tessellation. For regular polygons, the angle sum around a vertex is always 360 degrees. This is because each interior angle of a regular polygon is the same, so when multiple regular polygons meet at a vertex in a tessellation, the angles add up to 360 degrees.
What regular polygons fit around a vertex point?
Regular polygons that can fit around a vertex point must have interior angles that add up to 360 degrees when placed around that point. The regular polygons that meet this criterion are the triangle (60 degrees), square (90 degrees), pentagon (108 degrees), hexagon (120 degrees), and dodecagon (30 degrees). Other polygons with larger numbers of sides can also fit, provided their interior angles are divisors of 360 degrees. Thus, any regular polygon with an angle that divides 360 degrees can fit around a vertex point.
What following polygons can form a regular tessellation?
Regular tessellations can be formed by three types of polygons: equilateral triangles, squares, and regular hexagons. These shapes can cover a plane without gaps or overlaps, as their internal angles appropriately fit together. Other polygons, such as pentagons or heptagons, do not create a regular tessellation because their angles do not allow for a perfect fit around a point.
Which polygons cannot be used to form a regular tesselation?
Most regular polygons will not tessellate but if their interior angles is a factor of 360 degrees then they will tessellate or if their angles around a point add up to 360 degrees then they also will tessellate.
Will a regular polygon tile?
There are only three regular polygons which with tile. These a re a triangle, quadrilateral (square) and hexagon.This is because if there are n tiles meeting at a point, then the sum of the angles around that point must be 360 degrees - otherwise the polygons will overlap. The only regular polygons with interior angles that are factors of 360 are the ones mentioned above.
In a tessellation the angles of the regular polygons around a given vertex what do they always add up to?
They add to 360 degrees.
Why will only three of the regular polygons tessellate the plane?
The tessellating polygons must meet at a point. At that point, the sum of the interior angles of the polygons must 360 degrees - the sum of angles around any point. Therefore, each interior angle must divide 360 evenly. There is no 1 or 2 sided polygon. The interior angle of a regular pentagon is 108 degrees which does not divide 360 degrees. The interior angles of regular polygons with 7 or more sides lie in the range (120, 180) degrees and so cannot divide 360.That leaves regular polygons with 3, 4 or 6 sides.
What famous Greek mathematician came up with an approximate value for pi by circumscribing circles in and around regular polygons?
It was Archimedes.
Explain why regular polygons with more than 6 sides will not tessellate?
The tessellating polygons must meet at a point. At that point, the sum of the interior angles of the polygons must 360 degrees - the sum of angles around any point. Therefore, each interior angle must divide 360 evenly. The interior angles of regular polygons with 7 or more sides lie in the range (120, 180) degrees and so cannot divide 360.
What ancient Greek mathematician came up with an approximate value for pi by circumscribing and inscribing circles in and around regular polygons?
Archimedes (287-212 BC) was the first to estimate π rigorously. He realized that its magnitude can be bounded from below and above by inscribing circles in regular polygons and calculating the outer and inner polygons' respective perimeters. By using the equivalent of 96-sided polygons, he proved that 310/71< π < 31/7. The average of these values is about 3.14185.
What is the name of the tessellation made with more than one regular polygon?
A tessellation made up of two or more regular polygons is referred to as a semi-regular tessellation. The eight semi-regular tessellations are known as:3.3.3.3.6, 3.3.3.4.4, 3.3.4.3.4, 3.4.6.43.6.3.6, 3.12.12, 4.6.12, 4.8.8.The numbers refer to the number of sides of polygons around each vertex, starting with the polygon with the fewest number of sides.
