Lucas N. H. Bunt - The Historical Roots of Elementary Mathematics
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- Book:The Historical Roots of Elementary Mathematics
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Where proofs or methods of thinking are required, we have not attempted to supply all the steps or alternate solutions. We encourage our readers to be different and inventive. Wherever errors are found we would be pleased to be told.
- 2
- (a)
- (b)
- (d)
- (a)
- 3
- 20,507.
- 2,000,000.
- 100,000.
- 4 7. 10.
- 5
None. 45. - 6
Change each symbol to one of the next higher denomination.
- 1
- 3
- 1
- (c)
- (c)
- 2
- (c)
Answer: 40136
- (c)
- 3 Yes. If the larger number is used for the multiplier, the problem requires 9 doublings; if the smaller number is used, only 5 doublings are required.
- 5
- (c)
Hence, 242 11 = 2 + 4 + 16 = 22.
- (c)
- 6
- (a) 15 = 23 + 22 + 21 + 20.
- (c) 22 = 24 + 22 + 21.
- (e) 16 = 24.
- (g) 968 = 29 + 28 + 27 + 26 + 23.
Hence,
.
Hence,
.
Hence,
Hence,
Hence,
Hence,
- (a)
- (c)
.
- (a)
- (a)
- (c)
- (a)
- (c) If m is even then
, n an integer, and 
is already a unit fraction.
- (c) If m is even then
- (c) Let
Apply part to 
- (c) Let
- Let n = am + b , 1
b < m . Then 
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