Mathematics, Stretchy Calculator

.....An analog device for teaching multiplication and division, ratios and proportions, and squares and square roots. .Useful for teaching basic math skills, as a batteryless calculator in third world countries. Modern digital calculators work invisibly, providing answers but no insight into how the answers are derived. .This device is designed to help the student understanding the fundamentals of mathematics and why the answers increase or decrease in the way that they do.

.....The Stretchy™ calculator has numerical scales on a stretchable rubber band and on a fixed scale, and is used by pulling the rubber band while holding the calculator by the large hole. .The "1" on the rubber band is the index, and is important in almost every calculation.

.....Like a conventional slide rule, the calculator's accuracy is within 2-3 decimal places by the user mentally keeping track of the decimal place. .The calculator's surgical rubber band can stretch slightly beyond 10x, therefore in many cases the answer can be read adjacent the 10 on the fixed scale, rather than adjacent to the 1, for more accuracy.

Stretchy™ analog calculator operation:

MULTIPLICATION: .To multiply X times Y (X x Y, or XY), pull the rubber band until the index (the "1" on the rubber band) is next to the X value on the fixed scale. Opposite the Y value on the rubber band, read the answer on the fixed scale. .The animation illustrates two examples, 2 x 4 = 8, and 3 x 2 = 6.

DIVISION: .To divide X by Y (X ÷ Y, or X/Y), set the Y value on the rubber band next to the X value on the fixed scale. Read the answer, on the fixed scale, next to the index on the rubber band. Example: 8 ÷ 4. .Set the 4 on the rubber band next to the 8 on the fixed scale. .Adjacent to the index on the rubber band, read the answer 2 on the fixed scale.

RATIOS: X/Y: .Example, to set up a ratio of 2/5, stretch the rubber band until the 2 on the rubber band is adjacent to the 5 on the fixed scale, then adjacent to the 1 on the fixed scale, read 4/10 on the rubber band (or for more accuracy, adjacent to the 10 on the fixed scale, read 4 on the rubber band, and mentally shift the decimal to yield 0.4).

PROPORTIONS: .(X/Y) x N: .Example: (2/3) x N. .Stretch the rubber band to make the 2 on the rubber band line up with the 3 on the fixed scale. .Then, using the numbers on the fixed scale, read to the right to find 2/3 the value of any number on the fixed scale. Ex.: (2/3)2 = 1-1/3; .(2/3)3 = 2; .(2/3)4 = 2-2/3; .(2/3)6 = 4; .(2/3)9 = 6.

SQUARES:. X2: .To square X, set the index ("1" on the rubber band) adjacent to the value of X on the fixed scale. .Adjacent to the value of X on the rubber band, read the answer on the fixed scale. .Example: 3 squared: set the index on the rubber band adjacent to 3 on the fixed scale, and adjacent to the 3 on the rubber band, read the answer 9 on the fixed scale.

SQUARE ROOTS: .To take the square root of X, stretch the rubber band until the same value on the fixed scale (adjacent to the index on the rubber band), and which is on the rubber band, lines up adjacent to the value of X on the fixed scale. .Example: to find the square root of 9, stretch the rubber band until you find that the value on the fixed scale lines up with the index on the rubber band at the same time the same value, 3 on the rubber band, lines up with the 9 on the fixed scale. Only when the rubber band is stretched so that the 3 on the fixed scale lines up with the index on the rubber band, will the same value (3) on the rubber band line up with the 9 on the fixed scale. Therefore, the square root of 9 = 3..

DECIMAL EQUIVALENTS: .To convert X/Y, set X on the rubber band adjacent to Y on the fixed scale, then adjacent to "1" on the fixed scale read the decimal equivalent on the rubber band. .Example: 2/3: set the 2 on the rubber band adjacent to 3 on the fixed scale. Adjacent to 1 on the fixed scale (or 10 for more accuracy) read 0.66 on the rubber band.

FRACTIONAL EQUIVALENTS: .To convert a number in decimal form, set the number on the rubber band adjacent the 1 or 10 on the fixed scale, and find the pair of numbers that most nearly align with each other. .Notice, for example, that when calculating the fractional equivalent of 0.333, the answers of 3/9, 2/6 and 1/3 are all equivalent.