History of Mathematics

Homework Assignment 1

Prepared by:

Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York 11451

email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk/

1. The decimal system is based on the idea that:

374 represents 3(10)2 + 7(10)1 + 4(10)0

since (10)2 is defined to mean 10 (10) = 100

we have 374 represents 300 + 70 + 4 which is the number three hundred seventy four.

The reason we use powers of 10 is that in the decimal system we have 10 symbols including the symbol for zero.

Assuming the the digits 0, 1, 2, ...., 9 have their usual meaning and using the ideas above:

a. What number (write it down in words) is represented by:

324 in a system with 5 symbols (0, 1, 2, 3, 4).

b. What number (write it down is words) is represented by:

1011111 in a system with 2 symbols (0, 1).

c. What number (write it down in words) is represented by:

1202 in a system with 3 symbols (0, 1, 2).

3. What number is represented (write it down in words and Hindu-arabic symbols) by the following expressions in Roman:

a. XL

b. MCIX

c. CCCXXXIV

4. What number is representecd by the Egyptian number:

5. Do you think cats and dogs "think" about mathematics?