Results

**1 - 2**of**2**### Exact Arithmetic Using the Golden Ratio

, 1999

"... : The usual approach to real arithmetic on computers consists of using oating point approximations. Unfortunately, oating point arithmetic can sometimes produce wildly erroneous results. One alternative approach is to use exact real arithmetic. Exact real arithmetic allows exact real number computat ..."

Abstract
- Add to MetaCart

: The usual approach to real arithmetic on computers consists of using oating point approximations. Unfortunately, oating point arithmetic can sometimes produce wildly erroneous results. One alternative approach is to use exact real arithmetic. Exact real arithmetic allows exact real number computation to be performed without the roundo errors characteristic of other methods. Conventional representations such as decimal and binary notation are inadequate for this purpose. We consider an alternative representation of reals, using the golden ratio. Firstly we look at the golden ratio and its relation to the Fibonacci series, nding some interesting identities. Then we implement algorithms for basic arithmetic operations, trigonometric and logarithmic functions, conversion and integration. These include new algorithms for addition, multiplication, multiplication by 2, division by 2 and manipulating nite and innite streams. Acknowledgements I would especially like to than my supe...