MAT222 photography assignment

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Peace on Earth

This 2-dimensional Christmas light display is designed to represent a 3-dimensional sphere using lines of latitude and longitude. The longitudinal line in the center is the diameter of the sphere. The image would have 2 lines of symmetry if the "Peace on Earth" banner were removed. It would have one at the diameter and one going through the center along a latitude line. 

Caption: : Lights on the Bay in Sandy Point

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Caption: : Symphony of Lights in Columbia, MD

Snowflake Symmetry

This Christmas light display shows an almost perfect line of symmetry going straight down through the center snowflake. There are a few bulbs out on either side of the large snowflake, making it slightly imperfect. If we look at the center snowflake, it has 6 small line segments going out from the center of the snowflake. There are 6 longer line segments that connect at the vertex to what appear to be right angles. The short segments are congruent to each other and the longer segments with the angles attached are congruent to each other. 

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This window contains 4 lines of symmetry. The window is made up of a large oval with 4 trapezoids around it. There are 8 shapes that initially appear to be trapezoids inside the large oval with a smaller oval in the center. If we look closer, however, the bases of the trapezoids are both slightly curved, making them non-polygons. The are concaved at the top and convexed at the bottom. The non-poloygon figures inside of the large oval are congruent to each other's opposite. The oval in the center is a reduction of the larger oval surrounding it. 

Looking through a window of geometry

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Not a polyhedron!

The sphere to the right is NOT a polyhedron. It does not have faces made up of polygons. This modern house decor was light enough to pick up, so assuming that the inside is hollow, the volume can be found if we measure the radius of the sphere, we can measure the volume by calculating 4/3πr^3 (this program does support fractions and subscripts...). 

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Caption: : Meems Bottom Covered Bridge in Mount Jackson, VA

This beautiful covered bridge was constructed in 1982 from materials cut and quarried nearby. The arches and wooden beams support the covered roof, which is designed in patters of squares and triangles. The support beams along the side are in the shape of what appears to be 45-45-90 triangles. The triangular beams along the top are obtuse triangles. There is a pair of parallel lines running down the center, where cars drive through. The bridge has beautiful symmetry on either side of it. The left side is a mirror image (reflection) of the right side. Each triangular beam along the sides are translated through the bridge, as are the triangular beams along the top. 

My favorite discovery while exploring VA.

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The road to symmetry lies ahead

Caption: : Meems Bottom Covered Bridge in Mount Jackson, VA

This image shows the Meems Bottom Covered Bridge from the outside. The entrance is a convex hexagon with one line of symmatry going straight down from the peak of the roof. The roof forms an obtuse angle. The siding is constructed of parallel lines. The bridge is a beautifully constructed geometric figure. Although it's hard to see, the opening on the other side of the bridge is a reduction of the opening on the side closest to the camera. 

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The building to the right is designed in a pattern of parallel and perpendicular lines. There are 4 lines that run parallel horizontally and 8 lines that run parallel vertically. The horizontal and vertical lines intersect to form 4 right angles, proving that they are perpendicular. The perpendicular transversal theorem states that if a transversal is perpendicular to one parallel line, it is perpendicular to the other parallel line. The two lines parallel to a third line theorem states that if two lines are parallel to the same line, then all 3 lines are parallel to each other.

Parallel and Perpendicular Lines

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This image shows how road signs are constructed using the strongest polygon in existence, the triangle. The triangles are lined up in a tessellation,  they form a repeating pattern with no gaps or overlaps. The triangles are isosceles right triangles. They likely form a 45-45-90 triangles. The horizontal parallel lines of the structure can be cut by the lines of the triangles (transversals). Therefore, the alternate interior angles, corresponding angles, and alternate exterior angles that are formed are congruent. The same side interior angles formed are supplementary. 

I was the passenger

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My dream chandelier

The chandelier to the right forms a right cone. The base is a circle and the lateral area is formed by a triangle that has been rotated around a vertical axis line (altitude). The 4 chains hold the chandelier to the ceiling  at the vertex of the cone. Each chain represents the slant height of the cone. Also worth noting is the beautiful wooden beams that run parallel to each other along the ceiling. 

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This is an example of unconditional love. Using inductive reasoning, it is logical to form the conjecture that this is where my happiness comes from. We could form the conditional statement, "If Grace is home, then Krystle is happy." This is a true conditional statement. The converse, "If Krystle is happy, then Grace is home" is not necessarily true, therefore, this is not a true biconditional statement. 

Unconditional love

Caption: : Me and my Amazing Grace