Well now, isn't this a cozy little cosmos

Special to The Times

Mind-bending science and folksy craft come together in "Crocheting the Hyperbolic Plane" -- and that's just the tip of the iceberg. This ingenious little exhibition at Machine Project, a weekends-only gallery in Silver Lake run by artist Mark Allen, reminds visitors of the sublime beauty of mundane reality. Inviting laypeople and hobbyists to see the world with fresh eyes, it also wreaks havoc on seemingly simple certainties, demonstrating that the imagination is a far more useful tool than it's often made out to be.

Organized by guest curators Margaret and Christine Wertheim of the Institute for Figuring, "Crocheting the Hyperbolic Plane" includes nearly 50 crocheted models, several concise wall texts and an informative five-page publication, "How to Make Your Own Hyperbolic Book." These elements explain -- without jargon and just a bit of hyperbole -- what hyperbolic planes are by telling the story of various attempts to create hand-held models of the abstract concept.

In a nutshell, hyperbolic planes are not flat, like those in Euclidean space, but are crenelated, like lettuce leaves and some types of kelp. The farther you move away from any point on a plane, the more the space around it expands. Since the late 1800s, scientists have been cutting and pasting paper hexagons, heptagons and triangles to illustrate this concept. Their models generally looked like deflated, discombobulated soccer balls and were too fragile to be used in classroom demonstrations.

In 1997, Cornell University mathematician Daina Taimina turned to crochet to make a model that allows viewers to see and touch the abstract properties of hyperbolic geometry. The various examples in the exhibition, crocheted by Taimina and members of the Institute for Figuring, illustrate complex trigonometric principles by adding stitches, in various progressions, to each row. What initially appear to be colorful cozies for Christmas ornaments are actually precise 3-D diagrams of post-Euclidean, post-Newtonian space, which, many scientists think, just might be the shape of the cosmos.

Machine Project, 1200-D N. Alvarado St., L.A., (213) 483-8761, through Aug. 14. Saturdays and Sundays only. www.machineproject.com and www.theiff.org

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Sass and smarts, inseparably twined

About 20 years ago, Kim Dingle's hyperactive imagination gave birth to "Priss." The bespectacled girl, dressed in her Sunday best, began appearing in the artist's paintings and installations, where she pummeled her pint-sized peers, made a mess of everything she touched and seemed to be the star-crossed stepchild of Shirley Temple and Calamity Jane.

Ellina Kevorkian's new works at Western Project pick up where Dingle left off. Imagine Priss as a twentysomething. Then add a sidekick whose fiery eyes fan the flames of her love of destruction. That gives you an idea of the playful mayhem that takes shape in "Love Poems for Infidels," Kevorkian's second solo show, which includes 10 paintings, two lacy costumes and a three-minute video set to a throbbing pop beat.

Most of Kevorkian's paintings depict her and her twin sister, Soseh. The blond and brunet are often dressed in silk finery as they stroll through lovely gardens, sneak down candlelit corridors and cut the throats of men who get in their way. The twins also cool their heels in an old-fashioned jail cell and lean stiffly against one another, like a pair of pretty corpses in a 19th century death portrait.

In other digitally enhanced canvases, they skinny dip among lily pads and engage in a hot embrace. Equally at home in images staged to resemble Pre-Raphaelite paintings and soft-core porn, they also appear in settings that recall Bible stories, Victorian novels, gothic nightmares, Shakespearean dramas, film noir fantasies, wild westerns and campy rehashes of all of the above.

Fact and fantasy dance around each other in the grainy, sepia-toned video, which pays homage to two of the sisters' ancestors, another pair of female twins who robbed trains in Texas in the 1800s. Kevorkian's outlandish realism redeems pop cliches, transforming well-worn poses into archetypes both silly and inspiring. Think "Thelma & Louise" meets "Deadwood" and you're on your way to getting the gist of Kevorkian's smart, sassy art.

Western Project, 3830 Main St., Culver City, (310) 838-0609, www.western-project.com, through Sept. 3. Closed Sundays and Mondays.

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From anonymous to knowable

Since the mid-20th century, the materials of choice for corporate lobbies around the globe have been stainless steel, polished granite and glass. As a result, few artists in North America and Europe use these refined substances in their work, certainly not in combination with one another.

At Christopher Grimes Gallery, five new steel, granite and glass sculptures by Brazilian artist Waltercio Caldas suggest that in South America such slick materials are not so explicitly linked to corporate design. That's partly because these byproducts of modern industrialism still evoke avant-garde optimism, if not utopian idealism. But it's also because of the light touch Caldas brings to them, transforming their impenetrable anonymity into visual shifts and perceptual conundrums.

Each of Caldas' table-size sculptures consists of a four-legged steel frame on which rests a rectangle or two of smoothly polished granite. Atop these sleek slabs, each of which is positioned slightly off-center, the artist has paired handcrafted goblets, polished rocks and spindly forms made of welded steel rods. Hanging from the ceiling are long strands of wool yarn.

Caldas uses negative space effectively, drawing viewers into his abstract arrangements by using two or three lines to suggest a plane or a few points to draw a line in the mind's eye. Initially, his multipart pieces look symmetrical, their doubled forms appearing to be mirror images of one another. But no two elements exactly match. Each is singular.

The visual paradoxes Caldas' sculptures embody carry through to their materials. Although made of the same stuff as corporate lobbies, they would not look good in such settings. Their off-kilter idiosyncrasy and human-scale approachability are antithetical to the streamlined design of high-end lobbies.

Christopher Grimes Gallery, 916 Colorado Ave., Santa Monica, (310) 587-3373, through Sept. 3. Closed Mondays. www.cgrimes.com

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Layer upon layer of references

Brian Fahlstrom's solo debut is a modest affair: five paintings unceremoniously installed in the small square room behind the front desk at Marc Foxx Gallery. It's also among the most memorable of the season: sophisticated, intimate, quirky.

The young artist layers paint with the best of them, brushing on extremely thin coats of, say, metallic vermillion, followed by several layers of various matte grays. This results in semi-translucent veils that seem to flicker, capturing and reflecting light as your eye travels across their sensuous surfaces.

Fahlstrom holds nothing back in terms of historical references. Borrowing freely from artists so renowned that it's hard to imagine anything new comparing favorably to their achievements, he manages to make paintings that are neither derivative nor academic.

The whiplash efficiency of Henri Toulouse-Lautrec and Edgar Degas lies behind the two smallest works, "To the Light of the Moon" and "Nine-Thousand Days." "End Theme" is a 2-foot-square knockout that resembles something Paul Cezanne and Wassily Kandinsky might have collaborated on. And the abstract rooster in the nearly 6-by-7-foot showstopper, "Final Theme," could be the offspring of Ed Ruscha and Jasper Johns.

As knowledgeable about history as they are dedicated to the pleasures of the present, Fahlstrom's paintings deliver considerable satisfactions and suggest a promising future.

Marc Foxx Gallery, 6150 Wilshire Blvd., L.A., (323) 857-5571, through Aug. 6. Closed Sundays and Mondays.

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