Euler’s Identity: eiπ + 1 = 0. Euler’s Identity is an Equation about constants π and e. Both are “Transcendental” quantities; in decimal form, their digits unspool into Infinity. And both are ubiquitous in scientific laws. But they seem to come from different realms: π (3.14159 …) governs the perfect Symmetry and closure of the Circle; it’s in Planetary Orbits, the endless up and down of light waves. e (2.71828 …) is the foundation of exponential growth, that accelerating trajectory of escape inherent to compound interest, nuclear fission, Moore’s law. It’s used to model everything that grows. What Euler showed is that π and e are deeply related, connected in a dimension perpendicular to the world of real things - a place measured in units of i, the square root of -1, which of course doesn’t … exist. Mathematicians call it an imaginary number. These diagrams are visual metaphors. Imagine a graph with real numbers on the horizontal axis and imaginary ones on the vertical. Exponential function, f(x) = ex, ordinarily it graphs as an upward swooping curve - the very paradigm of progress. But put i in there, Euler showed, and eix instead traces a circle around the origin - an endless wheel of Samsara intercepting Reality at –1 and +1. Add another axis for Time and it’s a helix winding into the Future; viewed from the side, that helix is an oscillating sine wave.The rest is easy: Take that function f(x) = eix, set x = π, and you get eiπ = -1. Rearrange terms and you have the famous identity: eiπ + 1 = 0. That’s the essence of Euler’s alchemy: By venturing off the real number line into this empyrean dimension, he showed that disruptive, exponential change (the land of e) reduces to infinite repetition (π). These diagrams combine the five most fundamental numbers in math - 0, 1, e, i, and π - in a relation of irreducible simplicity. e and π are infinitely long decimals with seemingly nothing in common, et they fit together perfectly - not to a few places, or a hundred, or a million, but all the way to forever.
You can take this farther, too. If you write that function above in a more general but still simple form as f(x) = e(zx), where z = (a + bi), what you get is no longer a circle but a logarithmic spiral, combining rotation and growth - now both at the same time- These graceful spirals are also found everywhere in Nature, from the whorls in a nautilus shell to the sweeping arms of Galaxies. And they’re related, in turn, to the Golden Ratio (yet another infinite decimal, 1.61803 …) and the Fibonacci Sequence of Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …). But the weirdest thing about Euler’s formula - given that it relies on imaginary numbers - is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems into more tractable algebra - like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digitize music, and it tames all manner of wavy things in quantum mechanics, electronics, and signal processing; without it, computers would not exist.
i donated blood today. feels good to finally be somebody’s type.
gabbie hanna
https://www.instagram.com/thepersonalquotes/
Kids Give Their Opinions About Marriage…
It is painful but ih my dear its gonna be safer for you and your heart
How do you even write in circular gallifreyan? I tried to learn but i don't understand
Here’s my go for a Sherman’s Gallifreyan guide:
You start with drawing a circle:
Then you will look from the chart below (It only has consonants I’ll explain how vowels work soon) what kind of circle represents the letter you want to write.
Consonants take one of four forms and have dots, lines or neither. So if you want to write J it’s only one floating circle, K is the same kind of circle but with two dots and S is a half of circle with three lines. There is no C so you must write S or K instead depending on the sound.
For example the letter H looks like that ↑. The yellow part is the circle and two lines for H and the white circle is the word circle. The lines can go anywhere and if there are more letters that have lines they can also share lines.
Vowels are much smaller circles than consonants. They are usually attached to the preceding consonant, but they can also float on their own.
Those small circles which I have painted red and blue are the vowels.The photo shows where do they attach to different consonants (red circles) and how do they work on their own (blue circles).
I have added I to go with the H so that they form the word Hi
Here is the same word, but the letters are now seperatery and H shares one line with I. Both ways are correct. A vowel must stand on its own only when it has no consonant to attach to (a word starts with a vowel or you have two vowels in a row). Double letters are denoted by double circles. Words are read and written anticlocwise starting from the bottom.
Sentences are contained within two circles. The outer circle is to just to contain the sentence and the inner circle has punctuations. To fill empty space the inner circle also has those half circles which I have painted greeen in the photo below. They have no true meaning and they are done simply for style.
“Empress of Mars”I have marked the reading order with numbers. Just like a word, you read them starting from the bottom and then proceeding around anticlockwise. So you start the reading from the bottom with E. Number two is M, three is P, four is R, five is E and six a double letter SS. Then you move on to the next word. As you can see the consonants share some lines so it doesn’t look messy.
Punctuation are added along the edge of the inner sentence circle.For example dot is a small circle in the inner circle and apostrophe has two lines that go from the inner circle to the word circle.
“The idiot’s lantern” The apostrophe is coloured yellow.
Since I write Circular Gallifreyan very often I have made a photoshop document which has the charts and some frequently used words
(“muista” is Finnish for “remember” if you wondered. It’s to remind me about those lines)
The hardest thing about writing Circular Gallifreyan is making it look good and getting all the letters to fit nicely. I usually leave the other halves of half circles till I have the whole text done and then erase then.
This is a screenshot I took while doing the all things end -quote. At that time it didn’t even have all of the circles so you can believe it’s hard to remember which ones to erase.
That’s the finished quote ↑. It has several sentences and they are placed the same way as words to sentences and letters to words.
That’s the basics of it. I hope this clears things up for you. If not then just ask more. I’m bad at explaining things so I hope this is not too confusing.
🖤apache tear + gentle form of obsidian, useful for mending sorrow and grounding + legend states this stone formed when the tears of weeping apache women fell to the ground as they mourned their dead warriors
🖤calendula (marigold) + often used in funerals and remembrance ceremonies, eases sorrow + closely tied to samhain and día de los muertos
🖤cemetery dirt + used in a variety of death rituals and spells + contacting the dead, banishment, protection, astral protection + various types have different effects, research ethical collection first
🖤copal + resin often burned for purification, grounding, exorcism + closely tied to día de los muertos
🖤cypress (tree of death) + used to honor the dead and mend associated sorrow + chips may be sprinkled over a grave to ease the pain of loved ones left behind and help the departed soul move on + classic symbol of mourning, commonly found in cemeteries
🖤frankincense + resin burned for consecration, exorcism, communing with the dead
🖤mullein (corpse candles) + can be used as a substitute for cemetery dirt + stalks are often used as wicks for homemade candles + used to invoke spirits and for divination
🖤myrrh + resin burned for purification, exorcism, healing sorrow + increases power of any incense, often paired with frankincense
🖤patchouli + can be used as a substitute for cemetery dirt + powerful, earthy musk when burned, useful for grounding in rituals
🖤poppy + suitable offering for the dead and many deities associated with such + brings peace to the deceased and loved ones
🖤rowan (mountain ash) + may be worn or planted near homes for protection + planted on graves to prevent haunting by departed spirits
🖤violet + legends tell of violets blooming on graves of virgins and saints + appropriate offering for the graves of children
🖤willow (witches aspirin) + traditional symbol of mourning as it “weeps” similarly to humans + used for protection and to commune with spirits + often found in cemeteries to soothe departed spirits
🖤wormwood + often used to summon spirits and commune with the dead + burned with sandalwood at night in cemeteries to conjure spirits
🖤yew + used for protection from evil and contacting the dead + often found in cemeteries and used in ancient roman funeral pyres
More inspiring quotes here