Wonder, the retired service dog for Ehlena Fry, 12, waits outside the Supreme Court on Oct. 31. Fry’s case emerged from her school’s refusal to allow Wonder to go to class. (Molly Riley/AP)

The erudite Justice Stephen G. Breyer, who speaks flawless French and is a recognized authority on architecture, showed yet another side during oral arguments at the Supreme Court on Monday.

“The clothes on the hanger do nothing; the clothes on the woman do everything,” Breyer opined. “And that is, I think, what fashion is about.”

“That’s so romantic!” interjected Justice Elena Kagan.

Some days at the Supreme Court are about class-action suits and habeas petitions. But on Monday, one case was about a little girl and her goldendoodle service dog named Wonder, and the other about the “stripes, chevrons and zig-zags” that make a cheerleader’s uniform distinctive from, say, a little black dress.

As might be imagined, each raises bigger issues.

The justices seemed to struggle with the fight between Varsity Brands, the behemoth in the multimillion-dollar cheerleading and dance uniform industry, and upstart Star Athletica.

Varsity has registered hundreds of copyrights of drawings and photographs of its uniforms and sued Star after its catalogue featured cheerleading uniforms that looked just like them.

The quandary is that while fabric designs, for instance, are eligible for copyright protection, garments themselves are not.

Justice Ruth Bader Ginsburg, a majorette back in her high school days when she was known as Kiki Bader, asked why it is not right to think of the case as Varsity’s copyrighted designs being imposed on a cheerleader’s dress.

Star’s attorney John J. Bursch said that what appear to be ornamental touches are integral to the design of the dress itself.

The positioning of the chevrons, stripes and color-blocks “creates the optical illusion that they are taller, that they’re slimmer, that they’re — they’re curvier,” Bursch said. “You know, all these functions work exactly the same way as camouflage.”

There was a lot more about camouflage in the hour-long argument, along with tuxedo T-shirts, modern artists and a particularly slimming dress that Stella McCartney designed for actress Kate Winslett.

Breyer tried to capture Bursch’s argument by invoking the French-American painter and sculptor.

“So when Marcel Duchamp has a shovel on the wall and says it’s a work of art, he can have a copyright as long as he doesn’t try to sue people who make shovels?” Breyer questioned.

“Exactly,” Bursch replied.

William Jay, representing Varsity, said the company’s copyrighted designs should be protected.

“Congress directed the copyright office and the courts to protect applied art as well as fine art,” Jay said. “Applied art is art applied to a useful article.”

But Kagan said the design of a cheerleader’s uniform seemed to be something different, “one that follows the figure of a human body, essentially. And that’s the difference between just a design of like stripes and zigzags and chevrons sort of abstractly, and then one that’s put on something that looks like a particular piece of apparel that’s meant to fit onto a human body in a particular way.”

Justice Sonia Sotomayor, who as a private lawyer defended the Italian designer Fendi against counterfeiters, told Jay that his position could endanger the tradition of low-cost garment makers copying high-fashion designs.

“We are now going to use copyright law to kill the knockoff industry,” she said. “I don’t know that that’s bad. I’m just saying.”

But Jay replied his client is not challenging “the shape, the cut, or anything like that” of their competitors’ uniforms. “It’s in the two-dimensional artwork that appears on the surface.”

The case is Star Athletica v. Varsity Brands.

In the case of the girl and her dog, the question was about the options open to Ehlena Fry and her parents when their local Michigan school district denied their request to allow Wonder to go to class with Ehlena.

The girl has cerebral palsy, which limits her motor skills but poses no cognitive impairment. The Frys bought Wonder so that Ehlena would not need a human to assist her in certain activities, such as picking up dropped items, opening and closing doors and helping the girl transfer to and from a toilet.

The school district refused to allow Wonder to work as a service dog, saying he would be a distraction in the classroom and that some children might be allergic. School officials eventually allowed a 30-day trial run, in which adults even observed Ehlena in the bathroom with Wonder.

Eventually, the district again said no. The Frys pulled her from class, home-schooled her for the next two years and then found a school district that welcomed both their daughter and her dog. Ehlena, now 12, no longer requires a dog to help her, and Wonder has moved into retirement as the family pet.

The legal issue is rather dry. Congress requires that parents negotiate special requests with school districts under the Individuals with Disabilities Education Act (IDEA), which requires schools to make sure all students receive a “free and appropriate education.”

Until that process is exhausted, suits under the Americans with Disabilities Act are not supposed to be entertained by the courts.

But the Frys say they are not asking the school system to come up with a plan for their daughter. They are seeking money for emotional damages and attorney fees, which are not remedies under IDEA.

And their attorney, Samuel R. Bagenstos, said they are seeking their rights under the ADA: “The rights that individuals with disabilities have to bring their service dogs to public facilities are the same in all public facilities. You have a service dog; you can bring it.”

The attorney representing the school district, Neal K. Katyal, said the idea behind IDEA is that Congress wanted negotiations between parents and school officials, rather than having decisions made by courts.

“A lawyer could walk in on Day One and sue for money damages, and then . . . extort or possibly leverage that into a better situation,” Katyal said.

Chief Justice John G. Roberts Jr. and Breyer seemed worried about that as well. But Roberts also said he did not know why parents should have to go through the IDEA process if it would be futile.

It would be “kind of a charade,” he said.