QUEST Geometry Scavenger HuntHISD Cluster Janet Araujo Ashley Ellis Nancy Noyola Erika Saldana FALL 2006
PointA point is identified with a number or a letter. It has no length or width, it just specifies an exact location. • Man made Example: Map • Maps often have locations marked with points or numbers, such as the buildings at U of H. • Textbook Example: The following is a diagram of points A, B, C, and Q: • Naturally occurring Example: Pupil in our eyes • The pupil in everyone’s eyes can be seen as the same shape of a point.
Parallel LinesTwo lines in the same plane which never intersect • Man made Example: Wooden planks. • The planks of wood are the same with and are place within the same distance, forming parallel lines. • These planks are found by the beach, on the boardwalk. • Textbook Example: Lines 1 and 2 below are parallel. • Naturally occurring Example: Lines on side of mountains. • Parallel lines are often found in rock climbing mountains.
Pythagorean TripleConsists of three positive integersa, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer K. • Textbook Example: Scatter plot of Pythagorean triples within 4500. A and B are represented on the axes, and C is the vector distance from zero. The symmetry line at 45 degrees is made because 3^2+4^2 is the same as 4^2+3^2. • Man made Example: Hand fan. • The fan has the same shape as that represented of the graph of the Pythagorean principles within 4500. • This fan can be commonly seen in flamenco performances. Naturally occurring Example: Stars in space The scattered stars look very similar to those points represented in the graph of the Pythagorean triple.
FractalA rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale • Man made Example: Chandelier • The chandelier shows the same shape in different sizes. • Chandeliers can be found in many homes. • Textbook Example: Almost similar shapes varying in sizes. • Naturally occurring Example: Ferns • Ferns often have the same shape repeated all over it.
OvalA curve resembling a squashed circle but, unlike the ellipse, without a precise mathematical definition. The word oval derived from the Latin word "ovus" for egg. Unlike ellipses, ovals sometimes have onlya single axis of reflection symmetry (instead of two). • Man made Example: Jewelry container shaped like an egg • The shape of an oval can best be represented by an egg because it only has one axis of symmetry • These can be found in many jewelry stores. • Textbook Example: Ovals are shapes often shaped like eggs with one symmetrical axis • Naturally occurring Example: Egg • This item is found in grocery stores and in most common households in the refrigerator.
Congruent ItemsTwo sets are congruent if they have the same shape and size, but are in different positions (for instance one may be rotated, flipped, or simply moved). • Man made Example: Doors • The doors in this two buildings next to each other show to be the same shape and size, therefore being congruent. • Textbook Example: Textbooks often show congruency with geometrical shapes such as triangles • Naturally Occurring Example: Flower • The petals on many flowers are the same shape and size in different positions.
Ray A "straight" line that begins at a certain point and extends forever in one direction. • Man made Example: Arrows • The arrow show a starting point and also show that they can go at a distance towards a certain direction. • Ancient arrows such as these are found at the museum. • Textbook Example: The following is a diagram of two rays: ray HG and ray AB • Naturally occurring Example: Manta Ray • The tail of the manta ray is an example of the way that rays are often drawn in geometry.
PentagonA pentagon is a five-sided polygon. • Man made Example: School Crossing sign. • The sing is a five sided polygon • These signs can be found nearby schools everywhere in the country. • Textbook Example: The regular pentagon is the regular polygon with five sides. • Naturally occurring Example: Flowers with five sides. • These five sided flowers can be found at Big Pocono State Park in Monroe County in northeastern Pennsylvania.
Ellipse Mussle- Naturally Occurring The mussel naturally has a closed curve and two fixed points that add up to the same value EllipseClosed curve, one of the conic sections of analytic geometry, consisting of all points whose distances from each of two fixed points (foci) add up to the same value. The midpoint between the foci is the center Bath tub- Man MadeThe bath tub is a close curve and has two fixed points that add up to the same value In a text book an Ellipse would look like this ->
PrismA general prism is a polyhedron possessing two congruent polygonalfaces and with all remaining faces parallelograms Man Made- Triangular PrismThis is a triangular prism because it has triangular base a translated copy and three faces joining corresponding sides. – Naturally Occurring: The iceberg is naturally shaped to resemble a prism. In a text book a triangular prism would look like the following:
Line A line is a straight one dimensional figure having no thickness and extending infinitely in both directions Naturally Occurring: Horizontal line of a Sunset During a sun set such as this one a line divides the earth from the sky Man Made – Power lines These power lines run in astraight line and extend infinitely in both directions In a text book a line would be represented like the following drawing:
Transversal Line A transversal line is a line which intersects each of a given set of other lines. It is also called a semisecant. Man Made – Power Lines The constant intersection of power lines convert each power line into a transversal line Naturally Occurring-The branches on the tree serve as transversal lines when they intersect with each other Text book model of a transversal line:
Quadrilateral A quadrilateral, sometimes also known as a tetragon or quadrangle is a four-sided polygon. Man made: Picture frame This picture represents a quadrilateral because it has four sides Naturally Occurring: The cracks in the mud form quadrilaterals Textbook example of different type of quadrilateral:
Similar ItemsThe quality or state of being of having the same resemblance, the items can be comparable and have a likeness Man Made: The model cars all have a similar resemblance Naturally Occurring: The forest is full of similar trees. Textbook example:
Cylinder The surface generated by a straight line intersecting and moving along a closed plane curve, the directrix, while remaining parallel to a fixed straight line that is not on or parallel to the plane of the directrix Naturally Occurring: The trunk of a tree is shaped into a cylinder. Man Made: Coke Can A coke can represents a cylinder because it has lines on its side intersecting and moving along its closed plane curve Textbook example of a cylinder:
Sphere A perfectly symmetrical, three-dimensional geometrical object. In mathematics, the term refers to the surface or boundary of a ball. Man Made: Ball A ball is perfectly symmetrical and a three dimensional figure that represents a man made sphere. Naturally Occurring: Moon The moon is a naturally occurring sphere in outer space. An example of a sphere in a text book:
Intersecting LinesLines that intersect in a point are called intersecting lines. • These are roads that are found all over our city. • Roads cross everywhere making intersections. • This is a map showing intersections. In a textbook we could see intersecting lines like this: 2. These are naturally occurring intersecting lines because the sun has made the shadows from one side.
AngleThe figure formed by two rays sharing a common endpoint, called the vertex of the angle. • This is an angle. This angle is man made. • The two lines meet at the corner. In a textbook we could see angles like this: 2. This is the mouth of an alligator. This is naturally occurring when it opens its mouth.
ChordA chord is the line segment joining two points on a curve. • This is a man made chord. The strings go • through the curves of the circle. In a textbook we could see a chord like this: 2. This can be considered a naturally occurring chord because the water makes chord that connects to both curves of the sun.
TangentThe tangent function is defined by tanx=(sinx)/(cosx), where sinx is the sine function and cosx is the cosine function. In a text book we could see a tangent like this. 1. This is a heart monitor. It creates a tangent as the line goes up and down. This tangent is considered man made because the machine is man made. 2. This can be a naturally occurring tangent We trace the cloud on top of the power line.
PlaneA plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. • This is a picture of a room. This is the floor • of the room and is a man made plane. In a textbook we could see a plane like this: 2. This is a picture of ground. This would be considered a plane and it is naturally occurring.
TriangleA three-sided polygon. 1. This is a yield sign. This is in the shape of a triangle and it is man made. In a textbook we could see a triangle like this. 2. This is the fin of a shark. It is in the shape of a triangle this is naturally occurring.
CircleA circle is the set of points in a plane that are equidistant from agiven point O. 1. This a ring. This is in the shape of a circle. This is a man made circle. In a textbook we could see a circle like this. 2. This is an eye pupil. It is in the shape of a circle. This is a naturally occurring circle.
CubeA three dimensional platonic solid composed of six square faces. 1. This is a Rubik’s cube. It is a man made cube. In a textbook we could see a cube like this: 2. These are stones shaped like cubes. They are naturally occurring cubes.
A rectangle having all four sides of equal length. MAN MADE The top of the table makes a square. NATURAL The shape in this rock is a square. TEXT BOOK SQUARE
A solid body having a circle for its base and sides inclined so as to meet at a point above the base. MAN MADE The shape on this guy’s head is a cone. NATURAL This volcano makes the shape of a cone. TEXT BOOK CONE
A plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve. MAN MADE The top of this makes the shape of a parabola. NATURAL The shape between the peaks of the mountains is a parabola. TEXT BOOK PARABOLA
Something shaped like a curve or arch. MAN MADE This is the Arc de Triomphe in France. NATURAL The shape in the rock wall is an arc. TEXT BOOK ARC
A solid having a polygonal base, and triangular sides that meet in a point. MAN MADE The shape of this building is a pyramid. NATURAL This rock is in the shape of a pyramid. TEXT BOOK PYRAMID
Two lines extending in the same direction, equidistant at all points, and never converging or diverging with a line intersecting at a 90 degree angle. MAN MADE The wood logs are in this shape. NATURAL The ground is the perpendicular transeversal, and the trees are the parallel lines. TEXT BOOK PARALLEL LINES CUT BY A PERPENDICULAR TRANSVERSAL
Two lines extending in the same direction, equidistant at all points, and never converging or diverging with a line intersecting at any angle except 90 degrees. MAN MADE The lines of the power lines make this. NATURAL The lines in the side of this mountain make this shape. TEXT BOOK PARALLEL LINES CUT BY A NON-PERPENDICULAR TRANSVERSAL
References • www.google.com • www.mathworld.com • www.wikipedia.org