# Collected mathematical papers by Arthur Cayley By Arthur Cayley

1. ON A THEOREM within the GEOMETRY OF place. [From the Cambridge Mathematical magazine, vol. II. (1841), pp. 267-271.] we suggest to use the next (new ?) theorem to the answer of 2 difficulties in Analytical Geometry. enable the syinhols a . ß , 7

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Sammi insists that his idea is a good one. Think of some examples of areas that would either support his idea or show that it is wrong. c. Jorge has a different idea. He says that because the formula for the area uses square numbers, you can “unsquare” the number. What do you think of Jorge’s idea? 36 Building Formulas Formulas and Geometry D To “unsquare” a number, mathematicians use the symbol ͙ළළ. It is usually read as taking the square root of instead of unsquaring. 8. Find the square root of each of the following numbers.

To convert Celsius temperatures to Fahrenheit temperatures, use this formula: 9 F ‫ ؍‬᎑᎑ 5 (C ؉ 32). You know, for example, that 0°C corresponds to 32°F. 1. The second formula is not correct! Write a letter to the company that produced the notebook to explain why. What mistake was made? 32 Building Formulas The length of time it takes a driver to stop a car is affected by how fast the car is going. Suppose the following formula finds the stopping distance in feet if you know the speed of the car.

Is Mohamed right? Explain. 56 Building Formulas Section A Patterns 1. Yes, they describe the same pattern. Here are some sample strategies you could use: Strategy 1 A pattern could be: Path 2 Path 3 Path 4 T ‫ ؍‬P ؉ 2 ؉ P can be explained as a row of P orange tiles, 2 white tiles, and another row of orange tiles. T ‫ ؍‬2P ؉ 2 can be explained as 2 rows of P orange tiles and 2 white tiles. T ‫ ؍‬2(P ؉ 1) can be explained as 2 rows of P orange tiles and a white tile. Strategy 2 P ؉ 2 ؉ P is the same as 2P ؉ 2, and this can also be written as 2(P ؉ 1).