## Sudoku for Dummies

The binary edition for those affected by number blindness.

## The Fascinating World of Runic Calendars

The Runic calendar, also referred to as a Rune almanac, served as a perpetual timekeeping tool throughout Northern Europe until the 19th century. Structured with lines of symbols, it marked significant astronomical events and celebrations, including solstices, equinoxes, and Christian holidays. These symbols were often etched onto parchment or carved into various materials such as wood, bone, or horn.

One of the most esteemed examples of these calendars is Worm’s Norwegian runic calendar from 1643, renowned for its bone craftsmanship. Danish Antiquarian Ole Worm featured it in his book “Fasti Danici, universam tempora computandi rationem antiquitus in Dania et vicinis regionibus observatam libris tribus exhibentes.” Although he extensively detailed the winter months in his work, he omitted details regarding the summer season. Fortunately, supplementary insights are provided through ‘runstavs’ and ‘primstavs.’ ‘Runstavs’ served as runic sticks used in divination practices, while ‘primstavs’ were Norwegian wooden calendar sticks primarily employed for timekeeping and weather prediction.

## Beyond 65 digits, π serves no practical purpose

For spatial engineers’ highest accuracy calculations, used in interplanetary navigation, 3.141592653589793 is more than sufficient. Let’s understand why more decimals aren’t needed.

Consider these examples:

• Voyager 1, the farthest spacecraft from Earth, is about 14.7 billion miles away. Using π rounded to the 15th decimal, the circumference of a circle with a radius of 30 billion miles would be off by less than half an inch.

• Earth’s circumference is roughly 24,900 miles. The discrepancy using limited π would be smaller than the size of a molecule, over 30,000 times thinner than a hair.

• The radius of the universe is about 46 billion light years. To calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, only 37 decimal places are necessary.

• With just 65 decimal places, we could determine the size of the observable universe within a Planck length, the shortest measurable distance.

While π’s digits are endless, for microscopic, macroscopic or cosmic endeavors, very few are necessary.

## Nearly Right

Did you know? When you calculate 45)/e6, you get around 1! This means a triangle with sides π2, e3, and √π5 is nearly a right triangle…

## Feynman π Point

The Feynman point occurs at the 762nd decimal of π, displaying six consecutive nines (999999). Named after physicist Richard Feynman, he humorously shared, “I once memorized 380 digits of π as a high-school kid. My ambitious goal was the 762nd decimal, where it goes ‘999999.’ I’d recite it, reach those six 9’s, and cheekily say, ‘and so on!’ implying π is rational (which it is not).

## Timeless Trigonometry: Plimpton 322’s Revolutionary Legacy in Mathematics

Plimpton 322,” a clay tablet originating from ancient Mesopotamia during the Old Babylonian period (1900-1600 BCE), precedes Hipparchus by over 1,000 years. This artifact not only provides novel avenues for contemporary mathematical research but also holds implications for mathematics education. The trigonometry revealed in “Plimpton 322” presents a more straightforward and precise approach, showcasing distinct advantages compared to our current methods.

## Who bestowed Denmark with its intricate numbering system?

The Danish numbering system for multiples of ten from 50 to 90 is intricate. “Halvtreds” for fifty is a combination of “halvtredje” (two and a half) and “sindstyve” (times 20), yielding 50.

Complexity deepens:
Sixty, “tres,” is “tre” (three) and “sindstyve” (3 times 20).
Seventy, “halvfjerds,” is “halvfjerde” (4-½) and “sindstyve” (3½ times 20).
Eighty, “firs,” is “fire” (four) and “sindstyve” (4 times 20).
Ninety, “halvfems,” is “halvfemte” (5-½) and “sindstyve” (4½ times 20).

Historically, Danish used “siutyugh” (six tens) until around 1300. A text found in the city of Flensborg from that era introduces multiples of 20. The vigesimal system likely started in Western Denmark and spread eastward.

Similarities exist in French, where “quatre-vingt” (80) and “quatre-vingt-dix” (90) are based on twenty. Vigesimal counting appears in various Indo-European languages, possibly influenced by pre-Celtic languages.

More number facts.

## Magic Multiplication Tables

A neat math trick to perform: ask someone to sketch an hexagon on a multiplication table, then instruct them to sum the numbers at its vertices. By sharing the result, you can deduce the central number of the hexagon. How? Simply divide the sum by 6.

Additionally, here’s a secret: it works with pentagons too!