Well, e.

Last post, I talked about e being used in other stuff. Well, the first example is this!!!

e^ia = cos a +isin a.

What?!?!?!?! That basically means that e to the power of sqrt(-1)*a (an angle expressed in radians/angles (but be sure to include the degree sign!)) equals the cosine of a plus sqrt(-1)*sin a. SEARCH IT UP, IF YOU DARE!!!

This is an important formula used in a lot of stuff. Even Euler used it: e^iπ + 1 = 0

Never mind, what about this? The prime density of the range 1 to x is x/lnx. WHAT?!?! Don’t worry. The prime density is the fraction of the number of primes from 1 to x divided by x. ln(x) is the natural logarithm, or log base e. So lne = 1. The prime density, represented as π(x), is approximately x/ln(x). What!!

Yes, that is a LOT of stuff, but you could just search it up online. But NEVER EVER TRUST WIKIPEDIA. How foolish I was to make an account!

Anyway, the next one o=is about how π is WRONG. See ya!

Eeeeeeeeek!

What is down the line of beauty, just underneath φ? It is, of course, e! By e! I don’t mean e factorial, but just e. e is a number of some confusing sort. e can be represented as:

e=lim x->infinity (1+1/x)^x

AAAAAAAAAAAAAAAAAAAAAAAAAAAA! Not to worry, it’s not as disgusting as it looks. Imagine it this way: you borrowed $100 from the author, and you have it for 1 year, and give it at the end of the year with 100% interest. You will give me 100(1+1) = $200 back.

Now imagine you paid quarterly for the year, with 25% interest. In the first quarter, that is $125, Halfway is $156.25, and at the end of the year, you have to pay me a tiny bit more that $244.14!!!!!

Tenthly (every 1.2 months) payment is a tiny bit more than $259.37. Now this is the crazy bit. You pay me every DAY, and I end up with more than $271.45. Phew! What if you paid me ALL THE TIME NON-STOP?!?! Then you will give me a little more than $271.82, or $100e!

That will give me $171.82 more than what I had before. Yeees, I’M RICH!!!!!! I AM SO TOTALLY THE RICHEST PERSON IN THE WORLD!!!!!!

Says you.

Money critic

Yes, THANK YOU! e isn’t just used in financial maths, but also in other stuff. Stick around …

I mean, where is this beautiful number even USED?!?!

Good question.

Good question.

The author

Yes, yes, thank you. Now, if you can remember ANYTHING from the post “Nothing beats the beauty of this!”, then you will know that φ is used in a lot of places and artwork. φ might be a drastic little number, but φ is very useful. For example, the Parthenon, which the top has crumbled a bit, if the top didn’t crumble, the rectangle of base equal to the base and height equal to the perpendicular height from the crumbled corner to the bottom, it’s coincidentally a Golden Rectangle.

Mona Lisa, the famous painting painted by Leonardo Da Vinci, has the Golden Ratio (aka φ) hidden inside the painting. It is believed that Da Vinci used the Golden Ratio to incorporate balance, harmony and beauty. What?

Flowers also use φ to decide how their petals grow. Also, shells like the Nautilus shell are based off φ.

Yes, φ is used everywhere. Can the human body POSSIBLY use φ???

This will be the final post about φ. I think I’ll write about e now. Not now, but NEXT TIME.

Next time! Next time! Don’t forget!

The White Witch, The Chronicles of Narnia: The Lion, The Witch, and the Wardrobe

Nothing beats the beauty of this!

What is the most beautiful number? It is, of course, phi. Also known as the golden ratio, it is represented by the Greek symbol φ , and is the most irrational of irrational numbers. φ can also be written as this:

(1+sqrt5)/2. This may look ugly, but it is it. φ is used everywhere, in buildings and artworks and even the Milky Way galaxy relates to it. φ isn’t just about buildings and artwork, but it is related to the Fibonacci sequence.

Here is a question: what starts with 1 1 2 3 5 8 13 21 34 55 89? It is, of course, the Fibonacci sequence. The spiral is also interesting, where you put two 1×1 squares together and put a square with dimensions 2×2 then 3×3 then 5×5 …

φ can also be represented as this ugly little thing:

φ = 1+1/ φ = 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( 1+1/( … and you’d never be able to get to the end!

This was Part 1. Get ready for Part 2. I GuaRanTEe that it will be awesome and awesome! SeE you.