Renzo Piano Building Workshop designed the “organic creature” in the courtyard of a 19th-century block to house the new headquarters of the Fondation Jérôme Seydoux-Pathé – dedicated to preserving the history of French film company and promoting cinematography.
…The art of inserting a building into an historical city block means engaging in an open, physical dialogue with those already there. Building onto an extant structure also presents an opportunity for a more widespread renovation project, a reclaiming of space. The new headquarters of the Fondation Jérôme Seydoux-Pathé is an unexpected presence, a curved volume one glimpses floating in the middle of the courtyard in which it sits, anchored on just a few supports. On the ground, there is a stand of birch trees, a floral island set in the dense mineral context of the city…
The only other thing that might surpass the weirdness of physics is the mind-bending, headache-inducing nature of math. So, here’s my top 10 unsettling math facts, along with brief explanations of what they mean.
10: i^2 = -1
Imaginary numbers feel like they
shouldn’t exist to begin with. After all, what would it mean to have
4+5i apples? Although they don’t make much sense in the real world,
complex numbers are incredibly useful, and pave the way for even
d/dx e^x = e^x
The function y=e^x is a strange one, because if you plotted the slope as a function of x, you would get y=e^x. Also, if you plotted the area underneath the line as a function of x, you would get y=e^x again! Aside from y=0, this is the only function that is a plot of its own area and slope.
8: 1 + ½ + 1/3 + ¼ + 1/5 + … =
Even though each term in the harmonic series gets smaller and smaller, the sum still goes off to infinity. Although this seems counter-intuitive, there’s a simple proof for it. It’s easy to see that the harmonic series is larger than 1 + ½ + ¼ + ¼ + 1/8 + 1/8 + 1/8 + 1/8 + …, which can be written as 1 + ½ + 2/4 + 4/8 + …, or 1 + ½ + ½ + ½ + …, which clearly goes to infinity. Since the harmonic series is larger, it too must tend to infinity.
Some infinities are bigger than others
You’d think that there’s nothing bigger than infinity, but this isn’t exactly the case. If you tried to pair off every natural number
(1,2,3, …) with an irrational number
π, …), you would find that there would always be some irrational numbers left over. This means that the infinite number of natural numbers is smaller than the infinite number of irrational numbers.
6: The halting problem
Imagine there’s a program H that can check to see if another program will run forever or not. Now let’s say there’s another program P. When P runs, it will use H to check if P will run forever or not. P then takes the result, and does the opposite of what it says. But this means that H didn’t correctly predict what P would do, which is a contradiction! So, H must be an impossible program to start with.
5: Russell’s paradox
Let’s say there’s a barber who only shaves everyone who doesn’t already shave themselves. Does the barber shave himself? If not, then he’s missing one person who doesn’t shave them self, but if so, he breaks his rule. This is the idea behind Russell’s paradox, which opened up a major contradiction in set theory that could only be fixed by changing axioms.
4: Fractal dimensions
Fractals are probably one of the most beautiful parts of math, but they can be very difficult to describe. A main issue is that fractals don’t have a clear number of dimensions. For instance, a Koch curve has zero volume if you tried measuring it using 2 dimensions, but it has an infinite length if you tried using 1 dimension. This isn’t very useful, so we instead use something in between 1 and 2 dimensions. It turns out, a Koch curve has about 1.26 dimensions.
3: e^(iπ) + 1 = 0
Euler’s identity is probably one of the most famous and beautiful math formulas that exist, combining e, i, and
π all into a short equality. More generally, the formula is e^(ix) = cos(x) + i sin(x), derived from the series expansion e^x = 1 + x + x^2/2 + x^3/3! +… . Although this might be the most elegant, I wouldn’t say this is the most uncomfortable math fact that exists.
2: i^i is real
Going straight from Euler’s identity, we can quickly prove something even more strange. We know that e^(iπ/2) = cos(π/2) + i sin(π/2) = i, so we can raise each side to the power i to get i^i = e^(i*iπ/2), or e^(-π/2). From this, we can say that i^i
≈ 0.208. Somehow, raising an imaginary number to an imaginary number makes a real number!
Gödel’s incompleteness theorems
These two theorems are tied for first, both stating the limitations of math as a whole. The first incompleteness theorem states that there will always be true mathematical statements that can never be proven. This gives mathematicians nightmares, since some facts of math can never be known for certain, and we have no way of figuring out which ones they are.
The second theorem is even scarier, though, which states that any logical system you create can never be proven to be
consistent. This basically means that all of math could be wrong, but the only way to be certain would be to find some contradiction. If math does work, we’ll never know it.
Think all mascaras are the same? Think again, friend-o. Wands come in all shapes and sizes, and for good reason: They all do something different. In this Sephora Glossy post, we shout out beauty brands showing us never-before-seen winks. BECKY PEDERSON
PILE ON VOLUME Urban Decay Perversion Mascara
There’s a reason the tagline for this baby is, “Bigger. Blacker. Badder.” The triple-black pigments in this formula yield some of the darkest lashes we’ve seen. The high-tech brush separates to hit every lash and build without clumping, so if you’re into intense eye-batting, this one’s for you.
FAUXGET ABOUT FALSIES Tarte Best in Faux Lash Extending Fibers
Inarguably, falsies look great on everyone, but not all of us are down with putting glue on our lids. Enter: Tarte. The nylon fibers in the mascara primer build on and sculpt natural lashes so they look full and fluttery. The traditional-shaped wand is easy to wedge on the base of your lashes and pull through to the tip for a flashier look.
FAN OUT SANS FALLOUT Lancôme Grandiôse
Ok, so, you know how horses have enviably long manes and eyelashes? Like, if horses were people, they’d be the prettiest people in the room, and you’d spend all your time secretly trying to mimic their looks? Well, Lancôme can’t help you with the mane, but they can help with the lashes: Their patented swan-neck brush is designed to intensify and fan out from root to tip without leaving behind mascara flakes.
WELL-ROUNDED DRAMA SEPHORA COLLECTION Outrageous Curl Dramatic Volume Mascara
If you are plagued with short, thin, or stick-straight lashes, this is the mascara for you. Unlike typical curling wands that are concave and sometimes hard to wield, this wand is shaped like a rounded hairbrush so you can hit every lash from a horizontal angle. It provides so much volume, it’s like getting a blowout for your lashes.
NATURALLY INTENSE Josie Maran Argan Black Oil Mascara
Leave it to Josie Maran to reinvent the mascara formula. Hers contains natural argan oil and bamboo to boost lash strength and prevent breakage—all while promising up to 24 hours of wear. Also, the innovative five-sphered brush volumizes and curls for maximum sass.
Can you do tutorials on how to do Christine's makeup? Thanks! :)
Hey! Since Uni and social life are very stressful right now, the tutorial does have to wait (I will do a video tutorial in my semester break, which will be in July / August), but I will do a written tutorial for now ;) I will write a step by step tutorial and put the items I used in brackets behind it.
1. Face: I started off with priming my face (Catrice pore refining anti-shine base) and applied my foundation (Catrice All Matt plus) with a beauty blender. Afterwards I applied my concealer (Catrice liquid camouflage) under my eyes in a V-shape and over any spots that I might have. Once the concealer is done, I set my make up with a tinted powder (Catrice Multi talent powder + make up).
2. Contour / Highlight / Blush: I apply my contour along my jawline, cheekbones and nose (NYX mosaic blush 04 peachy), I only do a light contour, since Christine doesn’t have any stand out features. My blush is mostly applied on the apples of my cheeks (Essence 02 bye-bye winter! (limited edition - wake me up spring)). On top of my cheekbone and down the bridge of my nose I put a light highlight (Rival de loop baked highlighter 01 moon dust).
3. Eyes / Eyebrows: I fill in my eyebrows with two different shades of brown eyebrow powder, one is a darker brown, used mostly for the end and the arch of my eyebrow, and the other one is a light brown which i use to fill in the front part of it (shiseido eyebrow and eyeliner compact in light brown). Afterwards I use a tinted eyebrow gel to keep my eyebrows in place (Catrice Eyebrow Filler). For eyeshadow, I firstly prime my eyelid (Rival de Loop eyeshadow base) and apply a light beige non-shimmery colour underneath my eyebrow (I use the light beige one from the Catrice Chocolate Nudes palette). Afterwards I apply a light pink eyeshadow on the entire eyelid (essence the velvets coralme maybe) and a darker brownish colour in my crease (the darkest one in the Catrice Chocolate Nudes palette). If you’re going for a smokey eye, apply light grey eyeshadow for the light pink one and black eyeshadow for the dark brownish one. The key here is to have a good and fluffy blending blush to blend it nicely together. Afterwards I line my eyes (essence waterproof eyeliner pen) and put some light beige on my waterline (essence long lasting eye pencil 10 almost famous).
4. Lashes / Lips: I use fake lashes for Christine, since mine are not stage-ready (Catrice Lash Couture Smokey Eyes Volume Lashes), and top them with mascara (Astor N°2 Volume and Curve Mascara). For my lips I use an raspberry coulored lipliner (trend it up 080) and a raspberry / dark pinkish lipstick (Clinique 51 matte plum). Afterwards just finish it off with some fixing spray (mine is from essence) and you’re good to go!! If you have any questions that can not wait until July, feel free to ask :)
(Disclaimer: I know not all brands are cruelty-free. I will not re-purchase their make up, but I will use it up. Also I am by no means a make up artist)
Felicity/Oliver, “One more chapter.” I really enjoy your writing, thanks for sharing it!
Oliver stood over Felicity’s shoulder, squinting in bafflement at the might-as-well-be-nonsense on the pages of her thick technical manual, and she was so absorbed she didn’t even notice. She was hunched on the bar stool, curved over the fat volume spread open on the breakfast bar, lips moving silently as her eyes rapidly scanned line after line about code or firewalls or… something.
He inhaled deeply. She didn’t move.
Tipping his head to the side, he exhaled gustily across the back of her neck, the little flyaway curls escaping from her topknot dancing in the wind of his breath. Her shoulders twitched and her neck broke out in goosebumps, but she paid him no further attention.
She flipped another page, gripping the edges of the book in her hands, and hunched closer. Oliver’s eyes narrowed, affront at being deliberately ignored flaring in his gut.
“Felicity,” he repeated, exasperated. “It’s after midnight, and we just spent ten hours chasing a psycho toymaker all over town. Come to bed.”
Her silent mouthing had turned to breathy murmuring, but she broke off long enough to mutter absently, “I have to be sure I know this, my recertification exam is in the morning and I haven’t had any time to study all week–Oliver!”
She shrieked as he snaked his arms around her waist and hauled her off the stool, huffing impatiently. His irritation itched worse as he realized she’d taken the book with her and was clutching it to her chest. Fine.
He hefted her half onto his shoulder, one arm dropping to brace under her thighs, and turned for the bedroom. “Nope. You need to sleep. I need to sleep. And I want you to sleep with me.”
She thumped him with an elbow, making him grunt, but not enough to loosen his hold as he strode leisurely down the hall to their room, catching the ktichen light switch with his own elbow on the way. “Wow, that was me-class, Oliver, but come on. If I don’t pass this test tomorrow they won’t hold another recertification in Starling for another six months. You can sleep without me!”
“I could,” he agreed mildly, using his foot to push the bedroom door open. He didn’t bother turning on the light, his bedside lamp already on. “But you’ve been exhausted since noon. And today kind of sucked. I’d like it to end in bed next to my girlfriend, please.”
He thought, for a moment, about dropping her on the bed to watch her bounce, but that wasn’t especially likely to win her over to his side of the argument. Instead, he set her down on his side of the bed, where the covers were already thrown back after he’d gotten tired of waiting for her to join him.
She pouted up at him, and he smiled charmingly and took his shirt off.
Felicity’s eyes traveled down his chest, and she sighed, shoulder slumping and technical manual falling to her lap. “That’s cheating.”
Smile widening to a grin, Oliver only nodded. “I really don’t care, if it works.”
Rolling her eyes she shoved her legs under the covers and scooched across the mattress to her side of the bed. “Fine. You win.”
Chuckling, Oliver shut off his lamp and crawled into bed, scooting in against Felicity’s back. He pressed a kiss against her shoulder, reached up to pull the hairband out of her hair, and settled his cheek into the pillows while he carefully finger combed her waves. He sighed deeply, content.
Until he realized there was faint blue light sneaking through the cracks of his eyelids.
Popping onto one elbow, he frowned down at her on her side, technical manual held open by her face and cell phone illuminating the pages. “One more chapter. One more and I swear I’ll sleep.”
Shaking his head, warm affection cresting over him like a wave to drown down his exasperation, Oliver leaned down and pressed a firm, lingering kiss to her temple. “One more chapter.”
He soaked in the heat of her body, curled into her back, and she kept her word.
One chapter later, she shut the book and set it with her phone on her nightstand, then turned in his arms and tangled their legs together.
Oliver fell asleep to her hand smoothing up and down his chest, and her heart beating sure and steady next to his.
Usually people associate evening smoky eyes with a sexy gray-and-black look, but tonight, we’re thinking pink. In this tutorial, Sephora PRO Artist Gilbert Soliz uses the SEPHORA COLLECTION Colorful 5 Eyeshadow Palette in No. 9 to demonstrate how to inject a touch of modern warmth to your nighttime eye. BECKY PEDERSON
1. Press Burgundy along the lash line using SEPHORA COLLECTION Pro Shader Brush #18. Then, use a clean brush to pull the shadow up the lid to the brow—without adding more to your brush—to create a gradation of color. “When you work with darker shades,” tips Gilbert, “you want to keep them close to the lash line to avoid looking garish…or like you have a black eye.” Once you’ve pulled up the color, use the #18 brush again to smudge out any imperfections.
3. Press Deep Grey along the lash line with SEPHORA COLLECTION Pro Shader Brush #18. Then, thicken the line on the outer corner of your eye. Pull the color along your lower lash line, stopping mid-eye.
From the moment our gazes first intersected
my pulse took off at an indeterminate instantaneous rate of change
and I already found myself trying to calculate
how long it would take to lay tangent to you.
Further back on my own number line,
I chose to wrap myself in worlds of whimsy,
lounge in lands of language.
I had always felt about as comfortable in a math class
as Harry Potter felt at Privet Drive,
and it was literature which taught me
that some infinities are bigger than others.
were the first boy to show me the mathematical implications of such;
the first equation I became so determined to solve
that I bothered to double check my work.
You plotted precise points along my perimeter
and found values for variables I hadn’t even realized I’d needed to solve for.
We accelerated exponentially,
spiraling out like the Fibonacci Sequence –
every step we took forward, a sum of where we’d already been.
You were a cosine function, constant in your fluctuation,
and I longed to be sine
so our points of intersection could be infinite,
stretching out in all directions.
I wanted to integrate the space between your heartbeats,
calculate the area under the curve,
find the volume of the passion we shared as it spread into all four quadrants
and every time I was 95% confident that my feelings for you
had reached an absolute maximum
you found enough statistically significant evidence
to reject my original hypothesis.
You snagged my from my sanctuary of similes
and showed me the elegance of evaluation,
the beauty of a balanced equation,
the world’s carefully crafted congruence –
permutations and combinations that make up the very improbability of life and of love.
You taught me what it felt like to have within my veins
of a limit approaching infinity.
In the end, unfortunately,
fate chose not to make trigonometric functions of us.
Instead, we were like perpendicular lines:
destined to meet once
then grow farther apart.
Even so, I carry the lessons you graphed within me
much like you used to carry your calculator –
close to your heart, and always.
A Mathematical Love Letter, by Rachel R. Carroll