Pell is to silver as Fibonacci is to gold
As mentioned in the previous post, the ratio of consecutive Fibonacci numbers converges to the golden ratio. Is there a sequence whose ratios converge to the silver ratio the way ratios of Fibonacci numbers converge to the golden ratio? (If you’re not familiar with the silver ratio, you can read
Read moreOpenX uses AmpereOne-powered C3A instances on Google Cloud to drive sustainability and performance at scale
Find out how OpenX leverages AmpereOne-powered C3A instances on Google Cloud to enhance sustainability and performance. Continue reading OpenX uses AmpereOne-powered C3A instances on Google Cloud to drive sustainability and performance at scale on SitePoint.
Read moreMiles to kilometers
The number of kilometers in a mile is k = 1.609344 which is close to the golden ratio φ = 1.6180334. The ratio of consecutive Fibonacci numbers converges to φ, and so you can approximately convert miles to kilometers by multiplying by a Fibonacci number and dividing by the previous
Read moreAncient accurate approximation for sine
This post started out as a Twitter thread. The text below is the same as that of the thread after correcting an error in the first part of the thread. *** The following approximation for sin(x) is remarkably accurate for 0 < x < π. The approximation is so good
Read moreMentally multiply by π
This post will give three ways to multiply by π taken from [1]. Simplest approach Here’s a very simple observation about π : π ≈ 3 + 0.14 + 0.0014. So if you need to multiply by π, you need to multiply by 3 and by 14. Once you’ve multiplied
Read moreA better integral for the normal distribution
For a standard normal random variable Z, the probability that Z exceeds some cutoff z is given by If you wanted to compute this probability numerically, you could obviously evaluate its defining integral numerically. But as is often the case in numerical analysis, the most obvious approach is not the
Read moreDrawing with a compass on a globe
Take a compass and draw a circle on a globe. Then take the same compass, opened to the same width, and draw a circle on a flat piece of paper. Which circle has more area? If the circle is small compared to the radius of the globe, then the two
Read moreMobile Observability: monitoring performance through cracked screens, old batteries, and crappy Wi-Fi
Today we chat with Austin Emmons, an iOS developer at Embrace, where he spent time rebuilding their SDK to work with OpenTelemetry. He discusses the challenge of tracking performance and watching for edge cases when your app is deployed across dozens of devices with enormous variability in their hardware, software,
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