#curvature

[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:

[knotty-et-al]

Pseudosphere and dini surface

^ Visualization about the transformation of a pseudosphere into a dini surface.

v Pseudosphere

[blairelythere]

Sculpting my ass so I can sit on the faces of my lovers (and haters) 💗✨️

[th3-0bjectivist]

“Terra Panoramic” - Acrylic paint on canvas

[whats-in-a-sentence]

But the question of whether the Energizer Bunny could move forever in one direction and vanish into the darkness, or would one day circle around and catch you from behind – whether space goes on forever or wraps back like a video screen – is still completely open.¹⁴

14. So far, we've focused exclusively on the curvature of three-dimensional space – the curvature of the spatial slices in the spacetime loaf. However, although it's hard to picture, in all three cases of spatial curvature (positive, zero, negative), the whole four-dimensional spacetime is curved, with the degree of curvature becoming ever larger as we examine the universe ever closer to the big bang. In fact, near the moment of the big bang, the four-dimensional curvature of spacetime grows so large that Einstein's equations break down. We will discuss this further in later chapters.

"The Fabric of the Cosmos" - Brian Greene

[thethirdbear]

[art-of-mathematics]

Pseudosphere transforming into Dini surface (WIP)

Here is a gif to what I try to depict:

Great website:

[ordinary-beautiful]

Curved space

[screampotato]

Original photo by Apostolos Vamvouras

I'm fascinated by curves, surfaces and space.

[fashionfotorecccluse]

Spacetime

[raurquiz]

#happybirthday #lindahamilton #actress #sarahconnor #theterminator #terminator2 #judgmentday #darkfate #dantespeak #HillStreetBlues #BlackMoonRising #BeautyandtheBeast #MissinginAmerica #HomebyChristmas #Chuck #Defiance #LostGirl #Curvature #EasyDoesIt #ResidentAlien #Claws

[nothing-but-glitter-and-lashes]

hi

recently started wearing trousers to school instead of skirts. i was pretty nervous bc i hate how my thighs look, and the school skirt covers them so u can’t see when i sit down. but i wanted to wear trousers. wore them in 1 day and the girl who ive liked for literally forever said she liked how i looked in trousers. and she said (not in a weird way) that my legs are nice. my self esteem has been so boosted by this i feel so much more comfortable in trousers <3

(btw im a cis female at an all girls school. we do have trans kids but not many. there is a school uniform which is mostly skirt, but there is a trousers option. most people don’t wear trousers. the ones that do get picked on for being gay. it’s stupid. they’re literally trousers get over yourselves.)

[wikinley]

Offshore windpark in front of the Belgian coast perfectly shows the earth's curvature.

[whats-in-a-sentence]

If all the matter and energy in the universe were to be smeared uniformly throughout space, and if, after this was done, there turned out to be more than the so-called critical density of about .00000000000000000000001 (10^-23) grams in every cubic meter* – about five hydrogen atoms per cubic meter – Einstein's equations would yield a positive curvature for space; if there were less than the critical density, the equations would imply negative curvature; if there were exactly the critical density, the equations would tell us that space has no overall curvature.

* Today, matter in the universe is more abundant than radiation, so it's convenient to express the critical density in units most relevant for mass – grams per cubic meter. Note too that while 10^-23 grams per cubic meter might not sound like a low, there are many cubic meters of space out there in the cosmos. Moreover, the farther back in time you look, the smaller the space into which mass/energy is squeezed, so the denser the universe becomes.

"The Fabric of the Cosmos" - Brian Greene

[marcospevensie2]

[15beads]

Barbara Hepworth (1903 -1975)

Barbara Hepworth, Head (Mykonos), 1959-60 | Offer Waterman

Barbara Hepworth, Zennor, 1966 | RWA Bristol

Educator Resource Packet: Two Figures (Menhirs) by Barbara Hepworth | The Art Institute of Chicago

BARBARA HEPWORTH, Elegy III, 1966-67 | Mira Godard

Barbara Hepworth | Pace Gallery