Part 1Part 2 In the previous post, we created an approximation to i by iteratively solving Sum[j=0,n]{x_(j)*x_(n-j)} = 1 to construct a number which squares to our base 2 representation of -1, …111. The first few terms are: … (35/128) (5/16) (3/8) (1/2) (1) Some observations: it is tempting to simplify this to the standard… Continue reading Numeric approximations to the imaginary number: divergent series

# Month: September 2023

## Numeric approximations to the imaginary number: the imaginary value

Part 1 With a number for -1, we can calculate the value of i. In base 2, …111 =-1, so we need a number x such that x^2 = …111. We can multiply by term order to iteratively solve. For the first term: 1 = x0*x0 So x0=1 Second term: 1 = x1*1 + 1*x1… Continue reading Numeric approximations to the imaginary number: the imaginary value

## Numeric approximations to the imaginary number: representations of negative numbers

The biggest barrier to approximating i, the imaginary number, as we approximate pi is the lack of a number -1. It is not clear how to take the square root of a negative symbol. Interestingly, there are numeric representations of -1 in the left infinite numbers, the numbers that can continue to arbitrary large terms… Continue reading Numeric approximations to the imaginary number: representations of negative numbers