The Phoenician alphabet is a writing system exclusively representing consonants, requiring readers to infer vowel sounds. Beginning in the ninth century BC, adaptations of this alphabet thrived, including Greek, Old Italic, and Anatolian scripts. Its appealing feature was its phonetic nature, with each sound (including vowels) represented by a single symbol, simplifying learning to only a few dozen symbols.
Nested Penrose Triangles
This is an illusory geometric structure that cannot exist in our 3D world. Let’s Explore its captivating depths and intrigue.
Here’s how to create this impossible structure. Start by drawing two parallel lines spaced apart from each other and divide them into 7 equally spaced lines.
Then follow the visual steps A, B, C, and D illustrated below. At the beginning (fig. A), you will need to replicate the alignment of the 9 parallel lines three times while applying a 60-degree rotation to each one, finally arranging them to form a triangle. Subsequently, follow the visual directions in B and C to obtain the figure shown in fig. D.
At last, you can add color and gradients to the structure as illustrated below.
Discover prints and merchandise featuring this op art masterpiece at my online gallery.
Topological Oddity: A Picture-Hanging Puzzle
Imagine the linear pattern as a hanging rope. Now, removing any one of these four nails will cause the entire rope to fall.
Illusory Structures
That’s what happens when you fall down a Penrose staircase…
Logarithmic and Fibonacci Spirals in Plant Phyllotaxis
Nature, particularly in plants, features logarithmic and Fibonacci spirals, exemplifying the elegance of natural design and the rhythmic dance of life, encompassing symmetry and other intriguing mathematical phenomena, including recursive functions.
Spiral patterns in plants emerge from their repetitive growth, where each turn closely mirrors the previous one with scaling or rotational adjustments. This growth process, common in nature and known as phyllotaxis, utilizes recursive functions, which can generate logarithmic and Fibonacci spiral patterns.
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 (π4+π5)/e6, you get around 1! This means a triangle with sides π2, e3, and √π5 is nearly a right triangle…
Balance & Unity: Hexagonal-Heptagonal Harmony
This heptagonal radial tessellation with hexagonal tiles not only serves as an aesthetically pleasing visual creation but also stands as a testament to the harmonious coexistence of mathematical precision and artistic expression.