Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ October ►
S	M	T	W	T	F	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30	31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Thursday, Oct. 17, 2024

11:25pm EDT

Members: 888

Guests: 2,183

Total Online: 3,071

Complex Numbers

by Spirit HalloWaltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Wordsmitty ✍️

a day ago
In response to "Can We?"

"corrugated ridges add strength " - and this is so you can't use your heel to crush it like you do a beer can.

1 Like

The Ghost of Jayne's Lost Sock

a day ago
In response to "Can We?"

The top and bottom seams fail first. *As reported by a friend who used to play "can bowling" with their coworkers (overnight shelf stockers at a discount grocery chain)

2 Like

Annette

a day ago
In response to "Can We?"

By the way:

"A significant new market for the can had become apparent after 1935 when, following the development of suitable internal coatings, the first beer cans were test marketed."

Evo lution of the tin can

1 Like

Annette

a day ago
In response to "Can We?"

As much as all the modern people decry canned foods, there seems to be a fierce competition on who gets to take credit for inventing tin cans.

In a small museum in the country side in France, I learned that French scientists finally achieved to retro-engineer the exact alloy for tin cans sometime in the 18th century. They claimed to have cracked a German secret.

This article that you quote credits an English person.

Funniest part is that I was convinced it was an AmeriCAN invention.

1 Like

Mummified_Mike

Oct 15, 2024 at 10:45am
In response to "Pushing the Button"

I wonder how many of the NASA guys involved in making the Apollo 11 decision had already read Crichton's The Andromeda Strain - published about 2 months before the Moon mission - and allowed it to influence their decision-making process?

1 Like

🌕 HuntersMoon

Oct 14, 2024 at 10:13am
In response to "DeTECHtion"

I had a B.S. detector but, with the election season here, it was more like a smoke detector with a weak battery - It just went on and on and on...

2 Like

Kåre Enga in Montana

Oct 13, 2024 at 6:18pm
In response to "Spit in the Ocean"

Worthy of a long comment. Yes, I could; but, I won't.

As for your list... I'm a bag of mixed nuts.

1 Like

WakeUpAndLive️🦇Elf'sSpell

Oct 13, 2024 at 11:48am
In response to "Revisited: "I Wood Knot""

1 Like

Elisa: Stik or Treat

Oct 12, 2024 at 10:46am
In response to "A Few Observations"

Oddly enough, I've encountered similar unisex style restrooms in the US. If you wander back up to Minnesota and go to the old Schell's brewery in New Ulm, they have them. Mi amor and I joke that they're likely the most progressive bathrooms in the entire (rural) county.

1 Like

Spirit HalloWaltz

Oct 12, 2024 at 10:13am
In response to "A Few Observations"

Elisa: Stik or Treat

, oh, yeah, I'd intended to mention those things but forgot.

On accessibility: Most of the places I visited were old; in some cases, older than the US. Spiral stairs, tiny passageways, multiple levels, and those blasted cobblestones. Difficult, if not impossible, to retrofit enlightened disability access features. The few places that were more modern did it better. That's one downside to the older stuff, I think.

Restrooms: tiny, few stalls, mostly unisex. The unisex thing doesn't bother me, and I expect it better accommodates trans people... but not disabilities. I saw pay-to-poo restrooms, but I managed to avoid having to use them.

Now, some people unfamiliar with Europe might wonder how the unisex bathrooms work. There's usually one or two urinals tucked behind a corner or something, but I imagine it might be shocking for some folks from the US to peer around a corner and see some dude standing at one. But the view is from the back, and it's not like you see anything important and/or disgusting. Also, the stalls don't have those flimsy walls with big gaps and cracks; each toilet stall is usually (for the ones I used) completely enclosed, with a locking door, and private. The hand-washing facilities are shared, and sometimes not even within the restroom itself. It is entirely possible that I missed some etiquette thing, but in general, one merely needs to acknowledge that, shockingly, we're all humans and we deal with waste in much the same ways. Basically, it's just different if you're used to the US (and mostly UK) segregated style, but it's not privacy-killing.

What was more shocking to me was the near-complete absence of bidets, even in hotel rooms.

October 12, 2024 at 8:39am

#1078145

A Few Observations

Tomorrow, I intend to get back to my usual annoying self here by posting a Revisited entry. As for today, well, I'm still in recovery, so I'll just summarize some of my observations on the trip that I may or may not have already blogged about (because I can't remember and can't be arsed to re-read what I've already posted).

I gained a greater appreciation of the intricacies of French wine. Contrary to French beliefs, it's not necessarily superior to other countries' wine, but it does take a different approach. Not that I know a whole lot of details; that takes years of study and practice. I don't mind practicing.

It's popular in some circles to tout the general superiority of Europe over the US. In other circles, the opposite is the case. As it turns out, in my opinion at least, that they're just different. Europe does some things better, like public transportation and healthcare delivery. The US does other things better, like... um... well, I can't think of anything offhand, but I'm pretty sure I would if I weren't so tired. I guess we invented the Internet and GPS, so there's that.

There are whole sections of Brussels where there are more chocolatiers on each block than all other businesses combined.

There are others that are pretty much entirely restaurants.

I gather that it is easier and takes less time to become a medical doctor anywhere than it does to become a chocolatier in Belgium.

Real estate prices (both rent and buy) are amazingly cheap there, compared to the US. At least in the country and small towns. And that's with a denser population.

Unlike my above comment about French wine, Belgian chocolate really is the best. Sorry, Switzerland. At least you won't send assassins after me for that observation. ...Right?

The old joke about how Brits think 100 miles is a long way, while Yanks think 100 years is a long time? It applies to mainland Europe as well. You just have to convert to SI units.

Best quote of the trip, by a Belgian tour guide, uttered between bites of a Belgian waffle topped with whipped cream and chocolate: "You Americans eat like you have free health care."

So that's all I'm going to post about the trip... unless, of course, something else reminds me of a thing I did there. Like I said, tomorrow, we're back to our regularly scheduled programming.

2 Like • Comment • View 4 comments

© Copyright 2024 Spirit HalloWaltz (UN: cathartes02 at Writing.Com). All rights reserved.
Spirit HalloWaltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://shop.writing.com/main/profile/blog/cathartes02/day/10-12-2024