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Time for Math Poster

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By Brigitte Bentele, Ron Lancaster

24-HOUR CIRCULAR CLOCKS are divided into 24 hours and display the time since midnight, which is when the day begins. Time is always written with four digits—00:00—but can be noted either with or without the colon. For example, 03:14 or 0314 represents the time of 3 hours and 14 minutes after midnight. One advantage of the 24-hour clock over the 12-hour clock is that there is no ambiguity about the actual time, which can be crucial in medicine and the military. On a 12-hour clock, 6:28 could refer to morning or evening, whereas 18:28 on a 24-hour clock is clearly in the evening. Of course, this is why we use AM and PM when writing times for a 12-hour clock.
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A Mathematical High Point - Poster

TAIPEI 101 has 101 floors above ground and five floors below. It was the first building in the world to be taller than half a kilometer and, from 2004 to 2010, it was the tallest building in the world. Taipei 101 set several records, including having the world’s fastest elevator. Using the building statistics given on the poster, challenge your students to calculate how far they can see from the top; how long it would take for the elevator to go from the ground floor to the 89th floor; or find the angle of depression from a particular spot on the roof. (Solutions provided)
Fibonacci Stays Here Poster

Fibonacci stays here
THE GOLDEN RATIO is also referred to as the golden section, the golden mean, the golden proportion, the extreme and mean ratio, and the divine proportion. It has been used to ensure beauty and balance in art, architecture, music and design for centuries.
Here, the ubiquitous Fibonacci sequence shows up where it is least expected: in the logo of a Chicago hotel. Your students can discover how to construct and measure a golden rectangle, determine where the golden ratio appears in the pentagon formed by a 5-pointed starfish, and apply graphs of polar equations. (Solutions provided.)
Patterns That Rock - Poster
PATTERS that rock
TRIANGULAR NUMBERS arise as solutions to many problems. The basic pattern that makes up almost every rock song ever recorded can be summed by saying, “1 and 2 and 3 and 4.” Musicians often say, “a 1 plus a 2 plus a 3 plus a 4,” which shows how to calculate the sequence of triangular numbers 1, 3, 6, 10, 15, 21, 36, 45, 55, 66, ....
Investigate triangular numbers, in particular, triangular numbers that are also perfect squares. Featured problems include finding the intersection of these two sets of numbers. (Solutions provided.)
Isn't Math Illuminating Poster
CIRCLES AND ELLIPSES are everywhere, even on the logo of Grand Central Terminal in New York City. The mathematics contained in this poster ranges from circumferences of circles, to frustums of cones, to ellipses, all found in the trappings of Grand Central Station. Ain't math grand? (Solutions provided.) $12.95
Star Dancers - Poster
A STAR POLYGON can be thought of as the set of points formed by connecting the vertices of a regular polygon in a special manner. This poster explores star polygons and discovers some of their properties, arriving at some interesting generalizations. Problems include proving the radian measure of the sum of the interior angles of a given star polygon; making a table that organizes information about the radian measure of interior star polygon angles; and whether or not it is possible to create a human hexagram, heptagram, or octagram. (Solutions provided.)
A Slice of Math Poster

TRUNCATING A CYLINDER is a technique often used in design to add beauty to an object that might otherwise be nondescript.
What happens when a cylinder gets truncated? Featured problems explore the situations that can arise when a plane intersects a cylinder. (Solutions provided.)
Math Meets Art Poster

MATH meets ART
STARRY NIGHT At first glance, James Yamada’s Our Starry Night, is a black, 12-foot-tall sculpture with 1900 unlit colored LED lights on its two flat surfaces. As one passes through the sculpture’s rectangular passageway, however, patterns of light appear triggered by a metal detector hidden inside the structure’s casing.
Have your students seeing stars as they explore combinatorics, ellipses, matrices, and parametric equations stemming from this investigation of a publicly displayed sculpture featuring geometric star shapes. (Solutions provided.)
I ♥ Parabola - Poster
PARABOLA Bridges are physical manifestations of a parabola. The height-versustime graph of falling objects at or near the center of the earth can be modeled by a parabola as well. It is usually the first nonlinear curve that students study in algebra. A parabola can be defined as the locus of points equidistant from a point (called the focus) and a line (called the directrix). The parabola with vertex at the origin and opening upward has the equation 4py = x2, where p is a constant representing the distance from the focus to the vertex (or the vertex to the directrix). $10.95
I ♥ Logarithmic Spirals - Poster
LOGARITHMIC SPIRAL The logarithmic spiral is a polar curve whose equation is given by r = aebθ, where a and b are constants.

The nautilus shell is the best-known example of the logarithmic spiral found in nature, but flying animals will approach targets by using a logarithmic spiral pattern. Raptors will hawk prey, swifts will attack insects, and insects will approach a light source via a logarithmic spiral. Beaches can form in the shape of a logarithmic spiral, and the arms of tropical storms can also model this shape. The logarithmic spiral has close connections to the golden ratio.
I ♥ Truncated Icosahedrons - Poster
TRUNCATED ICOSAHEDRON An icosahedron is one of the five Platonic solids (tetrahedron, cube, octahedron, and dodecadhedron are the others). The 20 faces of the icosahedron are congruent equilateral triangles. If planes sliced the icosahedrons at the 1/3 point of each edge, each triangle would become a hexagon, and a pentagon would replace each vertex of the original icosahedron.

The soccer ball and the ball used in the Olympic sport of team handball is an example of a spherical rounded analog of a truncated icosahedron. The flexibility of the surface of these balls and the air pressure on their contents results in this familiar round shape.
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