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Snowflakes and Geometry

How geometrical terms relate to snowflakes

on 18 October 2012

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Transcript of Snowflakes and Geometry

Geometry How geometric terms
relate to snowflakes Angles Polygons Polygons Congruent Polygons Triangles Supplementary Angles Linear Pair Complementary Angles Vertical Angles Parallel Lines Symmetry Perpendicular Lines Lines and Symmetry A parallel could go on forever in both directions
and never intersect the other parallel line. The symbol for parallel lines is Perpendicular lines intersect at a right angle.
The symbol for perpendicular is Vertical angles are congruent angles formed at intersecting lines and share a vertex, but not a common side. A linear pair is a pair of angles that share a common side and add up to 180 degrees. Complementary angles are angles whose measures add up to 90 degrees. You can't create complementary angles using facet lines because the distance between each facet line is exactly 60 degrees on a perfectly symmetrical snow crystal. Supplementary angles are angles whose measures add up to 180 degrees. They can, but do not have to share a side. A polygon is a closed 2 dimensional figure with straight sides. They are often classified by the number of sides that they have. Congruent polygons are polygons with the same angles and side lengths, but may be rotated or reflected, or in a different location. Triangles are 3-sided polygons whose angles add up to 180 degrees. Reflective Symmetry Rotational Symmetry Right Triangles Equilateral Triangles Isosceles Triangles Parallel lines don't occur in snowflakes as much as you would think because the snow crystals initially form as hexagonal prisms with the facets branching off of it. Reflective Symmetry Reflective symmetry is when a half of an image is a reflection of the other. Not all snowflakes are symmetrical, but the ones that are usually have both reflective and rotational symmetry. Snowflakes become symmetrical even though each facet grows separately because they are exposed to the same conditions. Rotational Symmetry Rotational symmetry is when an image can be rotated and it still looks the same. Since the facets of a snowflake branch out from an original hexagonal prism, all of the facets share a common intersection point, or vertex. The facets create angles in between themselves. Straight Line = 180 degrees Facet Line 60 degree angle 120 degree angle This linear pair is made by the gap between one facet on the 60 degree angle and between 2 facets on the 120 degree angle. These are the only angle measures you can get for a linear pair using only facet lines on a common side. 60 degrees 30 degrees So to create complementary angles on this snowflake I used one facet space and half of the space between another pair of facets 120 degrees 60 degrees A snowflake starts off as a hexagonal prism with a base of a hexagon. Symmetrical snowflakes have a lot of congruent polygons because each facet coming out has identical polygons on it and there are six of them. Right triangles are triangles with one angle that is equal to 90 degrees. You can't make a right triangle using the facet lines because each one is 60 degrees so you have to take one and a half spaces between the facet lines. An equilateral triangle has equal side lengths and all the angles are 60 degrees It's easy to make an equilateral triangle on a symmetrical snowflake because the length of each facet is equal and they connect to the vertex at a 60 degree angle with the facet next to it, so all you have to do is connect the tips of the facets next to each other and you have an equilateral triangle. An isosceles triangle is a triangle with two sides of the same length and two angles that are the same. The other angle and side length is different. The pink sides are equal and so are the pink angles. The brown line and angle are the different ones. By Allison Kelley
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