WHAT IS A TESSELLATION? The mathematical description of a repeated figure that covers a surface is tessellation. Bathroom tile is an everyday example of this. The interlocking pattern of tiles fills the entire floor without leaving empty spaces. Mosaics are another example of repeated shapes used to fill a surface. A regular tessellation uses only one shape of a single size, but there are other styles that can use multiple shapes and sizes to fill an area. Some mathematicians work on three-dimensional problems as well, such as covering a soccer ball with different patterns of shapes. Examples of tessellations occur in nature, such as the way that volcanic rock fractures into roughly hexagonal shapes to create columns.
MATH IN EVERYDAY LIFE: People respond positively to very big numbers, so an internet provider might run a promotion offering 1025 hours of free Internet access. The small print reveals the offer is only good for 45 days. There are 1080 hours in 45 days, so customers would have to use their Internet access nearly 24/7 in order to take full advantage of the offer. Similarly, a food label that says a product is "90% fat free" will be more appealing than one that says it has "10% fat." People also lend more credence to exact numbers, preferring "50%" to the less specific "half." But it's easy to confuse precision with accuracy, such as with food packaging. Compare a soft drink that has 39 grams of sugar and 140 calories per serving to a fruit drink with 31 grams of sugar and 120 calories. But the serving size of the soft drink is 12 ounces, while the fruit drink is only 8 ounces. So ounce for ounce, the soft drink has fewer calories and less sugar than the fruit drink. A little math can help cut through the deception to obtain the information people want.
The American Mathematical Society and the Mathematical Association of America contributed to the information contained in the TV portion of this report.