#horizontal axis of symmetry

[math-journal2]

<— Unit 28: Part 3 — Unit 29 —>

Eq —> Directrix + Latus Rectum

Graph —> Eq

V + F —> Eq

Eq —> Graph

(x,y) + v + symmetry —> eq

V + Directrix —> Equation

Page 79

[art-of-mathematics]

I know I have drawn this shape so often already, but the process of drawing it is so soothing.

And for that, I have drawn a kind of step-by-step guide how to draw that shape in the top of this drawing:

(from left to right: ) [sorry in advance if I make it sound more complicated than it actually is. If you want to draw it, I would advice you to focus more on these illustrations rather than on my gibberish-text.]

1. draw a 2-dimensional Cartesian plane - or, in other words: just draw a cross like depicted

1.1. mark 2 points on the y-axis/vertical line with same distance to the coordinate origin, then mark 2 points on the x-axis/horizontal line with the same distance to the coordinate origin. (The markings on the y-axis need to be farther away from the origin than the markings of the x-axis)

2. connect the 4 marked points like depicted above. This is a function plot of a tractrix. (it has two mirror symmetry axes. )

3. draw an ellipse and connect the two markings on the x-axis. This becomes a kind of "belt" for the pseudosphere (4th picture)

4. part the ellipse into whatever-amount-you-want of partings (like you would cut a cake) and slightly mark these.

5. now imagine you cut that shape horizontally on the outer surface. (In the 5th picture I depicted that with red-ish pen across the pseudosphere. ) -

6. then the cut shape needs to be "(shape) shifted". For that we use a set of marked points we did in step 4). Furtherly, we "cut" the ellipse open, and push one end of it to the top, and the other end to the bottom. (depicted in picture 6 )

7. Then we connect the rest to get that shape:

[literaryvein-reblogs]

Some Greek Art Vocabulary

for your next poem/story

Alabastron - A small vase for olive oil, often scented.

Amphora - A two-handled terracotta storage jar used by the ancient Greeks to hold or measure oil, wine, or milk.

Calyx - The external, cup-shaped, leafy part of a flower.

Calyx-krater - A krater with handles in the cupped shape of a calyx.

Epitaph - A funerary inscription.

Krater - A large pottery vessel with a mouth broad enough to allow a jug to be dipped into it; used for mixing wine with water in ancient Greece.

Negative space - The area around the decorative subject on a work of art; the external or outside area that defines the subject.

Palmette - An ornament of radiating petals on a calyx-shaped or budlike base; along with the sphinx, palmettes often top Greek grave markers.

Positive space - The area on a work of art where the subject is represented; the internal area.

Registers - In art, horizontal bands of images that often appear in vertical series on walls, vases, and so forth.

Relief - A sculpted surface in which the decorations stand out, in varying degrees of depth; reliefs are meant to be viewed frontally, not in the round.

Sphinx - A fabled creature that is half human and half animal; in Greek art and legend the sphinx has the head and torso of a woman.

Stele - An upright slab of stone usually inscribed and sometimes decorated with designs or figures that are painted or carved in relief; used by the Greeks as grave markers or for displaying public notices.

Symmetry - The duplication of an image on either side of a real or imaginary central axis.

Terracotta - Clay that has been fired at a relatively low temperature, brownish-red or buff in color.

Source ⚜ More: Word Lists

[incorrect-multiverse]

Maura *texting*: Feeling :(

Jane *texting*: Turn that frown upside down.

Maura: The ‘(‘ would still look the same due to its horizontal symmetry.

Maura: :(

Jane: Reflect that frown along its vertical axis.

Maura: :)

Jane: :)

[incorrectkakagaiquotes]

Kakashi: :(

Gai: Turn that frown upside down!

Mirai: It would still look the same, due to its horizontal symmetry.

Tatsumi: Reflect that frown along its vertical axis!

Kakashi: :)

[queenclaudiabrown]

Connor: :(

Abby: Turn that frown upside down!

Nick: It would still look the same, due to its horizontal symmetry.

Sarah: Reflect that frown along its vertical axis.

Connor: :)

[wannabesucessful]

Bert: ☹️

Ernie: Turn that frown upside down!

Bert: It would still look the same, due to its horizontal symmetry.

Ernie: … Reflect that frown along its vertical axis!

Bert: 😊

[rogersip]

5 Ways to Center an Image in HTML

If you have a picture or image that you want to center, there are a few ways to do it. The first option is to use CSS. For instance, if you are using a flex-box, you can use the position property to center the image. You can also use the text-align property.

CSS transform property

CSS Transforms are used to modify the appearance of an element in a browser. They are also a great tool for creating an interactive project. For example, they can be used to make website dots blink quickly. By using transforms and transitions, you can ensure that animations are consistent and reliable.

In order to center an image in HTML, you will first need to wrap it in a container. The container can be a div or another block-level element. When the image is wrapped in a container, you can use CSS properties to center the image. You can then use margins or horizontal and vertical margins to adjust the position of the image.

The image's width must be smaller than the width of the parent element. It can be set to a fixed value or a percentage. There are also auto and margin options for the right and left sides of the image.

CSS position property

There are a number of ways to center an image in HTML. Some are simple to use, while others require extra CSS code. In this article, we'll take a look at five of them.

First, let's review the old standby, position absolute. This is probably the most useful way to center an image in HTML. By using a div and setting its width to a fixed percentage, you can center the image.

Next, we'll examine the flex property. This is a bit more complicated, but can do the same thing without the need to calculate margins.

Finally, we'll see what the object-position property can do. The flex property tells the browser that the div is a parent container and the image is its child. That's important to know because you'll need to wrap the image in the container before you can apply the flex property.

CSS text-align property

There are many ways to center an image in HTML, but one of the easiest is to use the text-align property. The text-align property is useful for aligning the inner content of block elements, such as images, in the horizontal direction. It is also useful for aligning text on a web page.

Another way to center an image is to wrap the image in a div container. You will need to set a height for the div, as well as a width. In this case, you can also set a fixed length.

For more complex alignments, you can also use internal CSS and flexbox. Flexbox is an exemplary example of CSS wizardry. Flexbox allows you to center an image and other elements in your div.

CSS flex-box

The CSS Flexbox is a great way to center an image in HTML. It allows you to center images horizontally and vertically. This is especially helpful when you want to create symmetry or balance. You can also center text in a flexbox.

The first step is to set the display property to "block". Then, you can add the margin property. This will instruct the web browser to apply equal margins on all sides of the element. There are two types of margins you can use: auto and auto-margin. If you are using auto-margin, you will need to change the display property to grid.

Next, you must create a div element that is smaller than the image. This div must have the place-items property set to center. Once this is done, you can use the translate method to position the div along the X-axis.

Properly centering an image in html

Centering an image in HTML can be challenging. There are various ways to center an image, but some strategies are considered more "proper" than others. Some of these techniques use HTML, while others require CSS. Generally, centering an image is done through a text-align property.

Inline images need different methods to be centered than block-level elements. For example, an image that is centered horizontally may need to be resized. An image that is centered vertically may need to be floated.

Another way to center an image in HTML is to wrap the image in a container. However, this strategy requires you to use an external CSS file. It will also change the appearance of the image on the screen. You should do this once, rather than repeatedly.

[oblivionscience]

Ienzo, texting Riku: Feeling :(

Riku: Turn that frown upside down

Ienzo: The "(" would still look the same due to its horizontal symmetry

Ienzo: :(

Riku: Reflect that frown along its vertical axis

Ienzo: :)

Riku: :)

[iamzlaw]

INKTOBER 2024 - 5 - BINOCULARS

"Maybe you're holding them wrong," said Ernest after Gerard had been silent for a while.

Next to him in the parked car, at the wheel, Gerard let out a heavy sigh, so heavy his shoulders went up and down from the weight of it.

"How could I possibly be holding these binoculars wrong, Ernie?"

"They could be upside down."

"No, they couldn't. This is two cylinders, each containing the same number of glass discs at the same points in them, and all those discs parallel to each other and carved according to central symmetry, with the same axis as the tube they're in, to which they are perpendicular. Basically, as long as those binoculars are horizontal, they cannot be upside down."

Gerard couldn't believe he had to explain something like this, but for Ernie, he always did. His incessant albeit most of the time senseless questioning had lead them to solve more cases than any other private investigation agency in the city. And not just the currently active ones: ever. The success of their business was a team effort and Gerard would never dream of pretending otherwise, as annoying as his partner may become, sometimes.

"They could be front to back."

Gerard clicked his tongue as he lowered the binoculars from his eyes, his irritation growing.

"Do you honestly think I wouldn't notice if the binoculars were front to back?"

"Well… Did you take the cover off, then?"

"YOU took the cover off, Ern'! It's literally still in your hand!"

Ernest looked down, opened his left fist, and what do you know: the binoculars' cover was there.

"Then why aren't you seeing anything?"

"Because it's pitch black, and nothing is happening yet. The culprit is most likely still waiting to be certain the whole house is sound asleep, that's all. Just be patient."

Ernest went back to being silent for a spell, but that did not last.

"Can I have a look?"

"No."

"Why not?"

"Do you remember what happened the last time you used the binoculars, Ernie?"

Ernest was thoughtful for a moment, his eyes quickly darting in all directions as he sifted through his memory. When he finally recalled what had happened, his face lit up for a second, before a pout distorted his lips.

"Well?" insisted Gerard.

"I burnt one of my eyes trying to look at the Sun because I was bored."

"And?"

"And I forgot to put the cover back when I put them down to go to the bathroom, and the place we were surveilling from took fire."

"And?"

"And I burned my hand with the binoculars after I'd put out the fire."

"Right."

"It's night; nothing like that could happen now," pleaded Ernest.

Gerard considered his friend's argument for while. He was not about to look at the Moon, was he? With a resigned sigh, he handed over the binoculars, which Ernie received like a child a present on Christmas morning. Clumsy, as always, he fumbled with them for a couple of seconds before bringing them to his eyes:

"Everything always looks so weird, through binoculars…"

"Ern'…"

"Yes, Ger'?"

"You're holding them wrong."

[qphamsblog]

Virtual Sketchbook 2:

Journaling

Principles of Design

Unity and Variety:

In art, unity is the harmony and consistency of the visual elements that evoke a shared feeling of oneness. On the other hand, variety adds a diverse elements to the artwork, making it more intriguing and captivating. A harmonious and compelling piece of art requires a balanced combination of both unity and variation, as too much variety can make a piece seem disorganized.

Pieter de Hooch, Interior of a Dutch House

This artwork balances unity and variety by enclosing all of the action in one room, it is not super crowded and the interactions between these people are simple and easy to comprehend. The artist introduces variety by adding various shapes and squares that vary in sizes and orientation. These shapes are drawn in an orderly manner, thus promoting unity.

2. Balance

The placement of components within a composition to create a sense of equilibrium between opposing factors is referred to as balance. It may be accomplished by using symmetry (which is the arrangement of elements so that they look symmetrical and harmonious when viewed from either side of a central axis) or asymmetry—the uneven placement of parts that still results in a composition that is both stable and aesthetically pleasing—can be used to establish balance.

The White House (symmetrical balance)

Edgar Degas, Jockeys Before the Race (asymmetrical balance since the left and rights aren't identical)

3. Emphasis and Subordination

Emphasis is a tool used by artists to draw our attention to specific areas within a piece. Several approaches, such as large size, bright colors, high contrast, and central location, can be used to accomplish this. A focal point is the area that receives emphasis when it is focused on a particular location or figure. Position, light-dark contrast, color intensity, and size are all crucial elements in emphasizing a piece of art and drawing the viewer's attention to the most important parts of the artwork. 

The artist emphasizes a specific tomato by making it the only green tomato out of all the red ones.

4. Directional Forces

Directional Forces direct the viewer's attention along specific paths. The axis of the form, the perceived continuation of existing lines, or the imagined link between similar or neighboring shapes can all be used to create implied directional lines. These directional forces help in giving the artwork a sense of flow and movement.

Dance of the Lupine

There is a horizontal directional force towards the top of the painting, a diagonal force down the middle from the top left to the bottom right of the painting, and the vertical line below the diagonal.

5. Repetition and Rhythm

The repetition of visual components may offer unity, continuity, flow, and emphasis to a composition. Patterns originate from the repeating arrangement of these pieces. Similarly, rhythm in visual art is produced by repeating elements with related modifications, providing a dynamic and unified visual experience.

FourShadowing

The overall art is somewhat the same, with some repetition and modifications in color/ objects in each piece.

6. Scale and Proportion

Scale refers to the relative size of one thing in relation to another, indicating how pieces within a composition relate to each other in terms of size. Proportion, on the other hand, specifies the size relationship of parts to a whole. Both scale and proportion are vital for establishing balance and harmony in art and design.

This artist uses proportion to create a comical attitude of this piece. This baby chicken is large in proportion to the man standing to the right. The chick is way out of proportion realistically, which creates a sarcastic response.

[math-journal2]

<— Unit 27: Part 3 —>

Trick

F + V —> Eq

F + e —> Eq

C, V, F —> Eq

Eq —> V, F, e

Non-Standard —> Standard

Page 76

[fanfics2747]

Deck9?!

"Playing cards are an integral part of American and global culture." This line began the proposal of Deck6, seen here.

The proposal lists several similarities between the original four suits, and it crafts one new suit for each color.

However, I thought "why not take it a step further?" and introduced a third color into the mix, while still preserving the values mentioned in the article.

Everyone, say hello to the Astral Deck.

Assessment of the existing suits

All four suits share some commonalities: Symmetrical on a vertical axis, composed of curves and straight lines as a single solid shape, short names composed of common words, and most intriguingly, all suits of a color having nearly-identical bases.

Deck6 also adds a new commonality: both colors have one suit with a single point on top, one suit with two points, and one suit with three points.

Do They Match?

My new color, the Yellow or Gold suits, follow all of these axioms.

They are symmetrical around the vertical axis (and the Cross, like the Diamond from the original set, has an additional horizontal axis of symmetry)

Each Yellow suit has the same bottom, with two points facing away from each other.

The names of the suits are "Arrow", "Cross", and "Star", which are simple yet descriptive monikers.

So I would say they do, in fact, fit in with Jim's additions as well as the original four.

Like its predecessor, most games are playable with no rule modifications.

Not Deck9?

My initial plan for the name was to use the straightforward naming convention established by Jim, but apparently people are actively hating something else called Deck9, so that isn't an option (for now, anyway - if they stop making Life Is Strange games, we might have a chance).

The (hopefully temporary) name is:

...based on the star and its derived symbols.

[sottosketch]

WEEK 5 22/08/2024

In this week's activity covers symmetry and grids, where we draw using grids for precision in our drawings. In our first exercise which we were tasked to draw an apple using a grid, I first started with vertical and horinztal lines, or the x and y axis. From there, I sketched the outline of the apple and proceeded to shade it. This acitivity was also about making symmetrical shapes such as an apple as a guide, and then we add complexity to it such as the shading and other details of the apple such as the leaves. This was a fun and interesting introduction to using a grid, and also a good drawing subject to ease in the idea of symmetry and grids. In my experience with this, I find it too be easy and relaxing.

In the second activity which follows the same formula as the previous activity. We were to draw a skull, that is more complex but also symmetrical just like the apple. Using my ruler, I made grid lines first starting from the center of horizontal and vertical lines, and added more lines as I go. From there, just like the apple, I proceeded to shade and add details that make the skull. I went heavy with the shading and use tissue to smudge part of the skull so that I can blend it. Overall, it was more challenging than the apple as it was more complex and detailed than before, but eventually a fun task in making further use of the grid and further learning the idea of symmetry through a more complex object.

In the last activity which is similar to the previous activities done, we were to draw a more and choose a more complex subject of things we are interested in, or pretty much anything. For this final exercise, I wanted to draw a picture of my family dog, Luna, who is a golden retriever. I wanted to draw something complex that has a lot of detail and also one that I really like. As part of the weeks idea and activity, I first formed a grid using my ruler and adding more lines wherever necessary and proceeded to draw and outline the sketch of my dog. From there, I used only a 6B pen to shade heavily or areas and add details. This was the most challenging exercise to do out of most activites as the drawing was quite complex and detailed and it took quite some time. However, considering it was complex and challenging, it was overcome from the learning experiences I had from putting in the work in previous weeks which I have learned a lot from.

Overall, in this week's activity, I have learned a lot about the use of grid and symmetry is applied through it. Grids are very helpful in learning how to draw if you are someone who cannot draw freehand especially if you cannot draw symmetrical objects well, but it can also be used for anyone at any level of drawing skills. Grids are there to provide as much precision as possible when drawing any subject.

[weekly--sketch--book--blog]

Weekly Sketchbook: Week 5 (Symmetry & Grids) Exercise 3 (Complex Symmetrical Drawing)

Reflections: In this week's activity we covered the basics of symmetry and grids, where we learned, how to use grids and x/y axis to precisely draw our subjects. In our first exercise, we were tasked to replicate a drawing of an apple, using a grid, firstly I a 4x4 grid system, which I later used to get closest to the proportions that I could. Started by lightly outlining the overall shape of the apple, and sketching in an outline of the highlights and shadows areas, where I will be shading later. After I was satisfied with the overall outline, I started adding a light shade and slowly added more and more layers to build, contrast and depth in the drawing. Switching between different pencil weights, to get lighter and darker tones. Also added some cross-hatching which I later on blended to get a smooth transition from dark to light. This exercise taught us, about symmetry and grids, which we used an apple which was a perfect example for learning symmetry.

In the second activity, we were given a skull reference, which we had to recreate, using a 5x4 grid system. Compared to the apple this was more complex as it had more intricate details. I started using my ruler to create a grid for the drawing, with a horizontal and then vertical line, and gradually added more lines as I went along. From then on I proceeded to sketch out a rough outline of the shape of the skull, as well as the features, like the nose and mouth, teeth, and eye sockets. Then slowly added some cross-hatching for a base layer then gradually aded more and more layers adding contrast. Throughout the drawing I used the Texturing techniques, that I had learnt from the previous weeks like hatching, smudging, stippling, and parallel lines.

In the third activity, we had to find a random complex subject to draw, so I decided to draw a penguin because I like penguins. I was bit confused, it I was required to use a grid or just x/y axis, ended up just using axis and slowly freehanding the outline of the penguin. From then on I started adding light cross-hatching, throughout the drawing, switching between 2b, 4b to create light and dark areas. The most challenging part was getting the proportions, even after finishing I still messed up the proportions.

Overall, all these activities taught me about how to precisely draw something, as well as all the previous exercises, helped add details and clarity for my drawings. Also gained more confidence in free handing, and drawing.

Date: 29/8/24

[jworthingtonreview]

Crafting Jewel-Box Gardens: Small Space Landscaping Ideas for Vegas Dwellers

Living in the shimmering oasis of Las Vegas often conjures up images of grandeur — sprawling resorts, opulent casinos, and pools that seem to stretch on forever under an eternal sun. It's a city known for its larger-than-life luxury. However, for the Vegas resident, home is where the heart is, and sometimes that space is small. But small doesn't have to mean mundane. You can transform your pint-sized patio or pocket garden into a luxurious outdoor haven that reflects the grandeur of your city's skyline. Here are some landscaping ideas that'll make you feel like you've struck gold, without needing a lot of it.

1. Jewel Tones and Vibrant Textures

Las Vegas's bold and bright personality is your inspiration. Incorporate jewel tones like emerald, sapphire, and amethyst into your small garden palette. Think about planting succulents and cacti that glisten in the sun, and foliage with rich textures that beckon touch. Layer greenery against the backdrop of a cerulean sky and watch as your small space transforms into a lush, sensory-rich respite.

2. Nighttime Lighting Magic

In Vegas, the party doesn't stop when the sun sets, and your garden can have the same flair. Intimate outdoor lighting can dramatically increase the perceived size of your space by drawing the eye towards the perimeters, making it feel like a larger expanse. String lights, lanterns, and discreet spotlights can give your garden a warm glow that's perfect for entertaining or unwinding after a long day.

3. Water Features

The soothing sound of water adds a layer of tranquility to your garden, creating an oasis within an oasis. A small fountain, a bubbling bowl, or even a mini koi pond can elevate your outdoor haven, making it the perfect place to relax amidst the high desert's hustle and bustle. Not to mention the added benefit of being a natural humidifier in those dry Vegas air months!

4. Selective Furnishings

It may be tempting to pack your small space with as much furniture and decor as possible, but less is often more. Choose a small selection of high-quality, comfortable outdoor furnishings. Opt for dual-purpose items like benches with storage or side tables that can also serve as extra seating. This selectivity allows for a more fluid and open space that feels less constrained.

5. Vertical Gardens

Vegas may not have much horizontal real estate to spare, but it certainly has the skies. Capitalize on that by installing a vertical garden. From simple trellises to sophisticated living walls, going vertical allows you to enjoy a variety of floral and edible treats without sacrificing ground space. It also creates a visually stimulating wall of green that can lend your small garden a loftier feel.

6. Sound Management

While a bit of city noise can be a part of the Vegas ambiance, your home garden should be a sanctuary from the sonic overload. Utilize sound-absorbing materials in your hardscaping when possible, and plant foliage around the borders to create a natural sound barrier. Additionally, consider the acoustics of any features you add, ensuring they contribute to a peaceful soundscape rather than adding to the noise.

7. Continuity and Symmetry

Creating a cohesive design in a small space can make it appear much larger. Choose a unifying theme for your garden, whether it's modern, zen, or traditional. Use repeating patterns and lines to provide a sense of continuity. Symmetry can also play a role in making the space seem more expansive. By mirroring elements across a central axis, the human brain registers a larger area than is actually there.

8. Space-Maximizing Plants

Select plants carefully for size, shape, and growth habit. For example, instead of a wide-spreading juniper, consider a columnar Italian cypress. Climbing roses or wisteria can add vertical interest without taking up floor space. And don't be afraid to use containers for smaller shrubs and trees. They can be moved around seasonally, and the spaces between them can be utilized for annuals or perennials.

9. Tech Integration

In the city that's home to the Consumer Electronics Show, why not bring a little tech into your garden design? Smart irrigation systems can ensure your plants are getting just the right amount of water, while outdoor speakers can provide a soundtrack to your outdoor life. Solar-powered lights and fountains not only help the environment but can also save on your power bill.

10. The Indoor-Outdoor Blend

Incorporate elements that blur the lines between the indoor and outdoor spaces, such as using the same flooring inside and out or placing potted plants near windows. This creates a sensory connection between the two areas, making your interior feel more spacious and your exterior more like a natural extension of your living area.

Small space doesn't mean you need to compromise on luxury. With thoughtful design, your tiny terrace or modest patio can become the jewel-box garden of your dreams, a personal retreat set against the glitz and glamour of Las Vegas. Remember, it's about creating an environment that speaks to you, that you love to be in, and that brings joy and a touch of the extraordinary to your everyday life.