Consider triangles, and consider geometry. These structures are here, literally and in spirit: The small interior benches are triangles; the shower is a triangle; the lampshades are triangles; the roof, too, is a triangle, though it’s an especially idiosyncratic example. Consisting of cedar shingles and wooden fascias, it folds downward just slightly and moves into an aggressive point in the backyard, where it hangs over a patio that expands into the grass. The roof looks almost like a spaceship, moving through the stars — except this spaceship stands among blowing leaves, and atop a hill. That is, it’s almost winter now, and the trees are beginning to prepare for it, shedding their green and yellow onto the ground, making a red circle around the wooden bench in the backyard. The circle of red leaves is fallen from the apple tree that stands behind the bench. The roof looks right at it.

Geometry can be confusing. There’s an adage that parents tell their children who are bad at geometry: If you’re bad at geometry, you’ll be good at algebra. If you’re bad at algebra, you’ll be good at geometry. For those kids in the first camp, who took to numbers rather than shapes, geometry might have felt forced, oddly unreal — inapplicable — with its sines and cosines, linear planes and precise measurements of the angles of a hexagon. The consequences of 3.14 and antipodal points might feel too abstract and separated from the ball you smack in a tennis match. It can be hard to see how math relates at all to this strange-ceilinged home on a hill.

But there is an approachable geometry at Frank Lloyd Wright’s Palmer House, situated at the top of Orchard Hills Drive, right on the edge of Ann Arbor’s city limits. When you drive up the lightly graveled driveway after curving back and forth a few times, you first notice the sharp edges of the outdoor garage. There’s a flat awning supported by triangular brick columns for vehicles, and for most cars, the back bumper will stick out just a little farther than the awning supports. Then you notice more shapes. There are the long and thin rectangular prisms of the stairs that lead to the front door, and a corner of the home stands to the left of the stairs (when you enter, you’ll then notice this is the kitchen), with two separate, horizontal rows of identical designs running through it. These are little windows cut into concrete blocks, and there are 40 of them that surround the kitchen, though only about half face out to the stairs by the entryway. This is a structure with a meticulousness for edges and lines. It feels hyperaware of where the eye will go, and where it wants to lead it. This home’s geometry leads first to the door.

The two front doors are in the French style and could pass as windows, if it weren’t for the dainty handles at waist level. Gary Cox, a resident of Plymouth, opens one. Cox is wearing a horizontally striped polo and blue jeans, and his rimless reading spectacles sit on a counter, facing the entryway.

Cox is the father of the current owner of the Palmer House, Jeffrey Schox. Schox, who does not live in Ann Arbor, is a graduate of the University of Michigan’s mechanical engineering program, and he now runs a patent law firm focused on startups; it has a sleek website that uses words like “transparency,” “passion” and “excellence.” He also has a soul patch, and resides in San Francisco.

Cox is responsible for most of the daily upkeep of the home, which now operates as a guest house year-round. (This is discounting assorted holidays. The family likes to spend their Christmases here.) He gives the rare tour and checks on the state of the infrastructure. Cox walks into the living room, where he begins to revel in his knowledge of the home. The room feels massive, though by square feet it’s little larger than most American lounges.

Cox meets each client before turning over the keys, and this is at least in part for vetting purposes. He reserves the right, he says, to turn a renter away at the door if he feels it’s necessary. But he has never done so, and these door greetings act more as an introduction to the home, which Cox says is the most difficult part of his job. To articulate to the clients what this all means; “to get the clients to … understand,” he says, requires this introduction. Cox speaks eloquently, at times impassionedly, when he talks about the Palmer House. He sometimes chuckles slightly as he recounts the details of the lives of the original owners. He has given this talk and tour many times — gave it just last week, to a group of students from the University’s Taubman College of Architecture and Urban Planning.

Keeping the name, “Palmer House,” is one of the stipulations for owning the home, which was designed by famed American architect Frank Lloyd Wright in the early 1950s. The home is under easement by the National Register of Historic Places, and beyond keeping the title, the new owners must also consult — and get approval from — the conservatory register to make any design changes, no matter how mundane. Every so often, the conservatory register makes a visit to inspect conditions. He speaks on these visits as if they were coffee dates among friends, chatting about the latest shift in furniture.

The title comes from the home’s original owners, William Palmer and his wife, Mary. Both were graduates of the University. William Palmer, known more commonly as Bill, or Billy, became a professor of economics after earning his master’s from the University in 1930. Mary Palmer, a pianist, graduated from the music theory program in 1937, and the couple married that same year.

It was Mary Palmer who reached out to Frank Lloyd Wright to design the home, and it was she who put in the work to see the initiative to completion — a trend true for many women with spectacled husbands who spend too much time in the study. The Palmers were living in a farm home on Geddes Avenue when they purchased two lots on Orchard Hills Drive with a generous donation from Mary Palmer’s father, who was involved in various banking and business interests. By then, they’d had their two children, Adrian in 1940 and Mary Louise in 1942. But it wasn’t just for them that they wanted the new home: The Palmers loved to entertain, and found it exceedingly difficult to do so at the more cramped estate. So the Palmers shopped around for an architect, looking at local homes for inspiration. They were especially attracted to the Margaret and Harry Towsley home on Vinewood Avenue, which was owned by and built for the Towsleys in 1932. Dr. Harry Towsley was a professor and a pediatrician at the University’s Medical School, while Margaret Towsley was an active community member, volunteering for Planned Parenthood, the community center and the Republican Party.

The Towsley home is arguably the beginning of the modernist architecture movement in Ann Arbor, with its flat roof and its garage that faced the street — a bold move then, and a first for the city. It was designed by Alden Dow, a Michigan architect who apprenticed under Wright. He would go on to design many prominent buildings in Ann Arbor, including the City Hall (on Huron Street, just down the street from those monstrous, ever-under-construction, brand-new student apartment buildings), the Ann Arbor District Library, the Matthaei Botanical Gardens and several on-campus facilities.

It was Bill Palmer’s brother, Carlos, who first suggested to the Palmers at a cocktail party that they seek out Dow’s mentor himself, Frank Lloyd Wright. Carlos Palmer was familiar with Wright’s work, and stated matter-of-factly their architect should be, “Wright, of course.”

Though Mary and Bill Palmer are no longer alive, conversations with the family regarding the house were recorded by Grant Hildebrand and synthesized into a book, published nearly a decade ago. Cox presents a volume to me, titled simply “Frank Lloyd Wright’s Palmer House,” with a sense of inherited pride. It rests on the living room coffee table, which is shaped as a parallelogram. These conversations illuminate a meticulousness by the Palmers in planning their home, especially from Mary Palmer’s end; she speaks in big ideas, and with poetic eloquence. She explained her first time walking through a Wright home with her husband as so:

“We sensed a new experience immediately on entering the carport and on into the loggia. … But inside there was warmth everywhere — in the fireplace, in the beautiful cypress throughout the house, and in the marvelous, warm floors.”

And yet she was not immediately sold on Wright. She explained, “I was attracted to his philosophy but … did I really want to live in one of those houses?” Here, she gets at something that feels tangible walking through this museum-home. The almost overbearing intention of the place doesn’t necessarily scream “homey.” “There was no basement rec room, no place that wasn’t absolutely beautiful,” remembers the daughter Mary Louise, describing the tenseness that comes with such beauty. Indeed, there’s a strict atmosphere in the air as we walk around; Cox has disallowed photographs of nearly all the interior, since it was stayed in just last night. When we walk into the bedrooms, with the bedding slightly unmade, he seems a bit embarrassed. He apologizes. The house is “not quite perfect right now.” Yet there’s a comfort in seeing the parallelogram beds imperfect, some humanity in those wrinkled sheets.

But on the drive home from a visit to a Wright house, Mary Palmer explained that she and Bill Palmer looked one another in the eyes and said, “Let’s get Mr. Wright,” and so they — or rather, she — did. Wright was 83 and it was May when Mary Palmer tracked him down at North Carolina State University. Wright was giving a lecture to their architectural school, and Palmer approached him and gave him extensive notes about the plot on Orchard Hills. Wright accepted the job, and replied to Palmer: “Now you go back to your husband and take care of those children. They need to live in one of my houses. I’ll take these things with me.”

Wright presented the Palmers with the original “plan geometry” in January 1951, and Mary, one of the few Wright homeowners to push back successfully on parts of his plan, made a few changes. Red brick was exchanged for the concrete originally proposed; a shower was added, an amenity which Wright was often reluctant to include in his homes, being a man of baths himself. After revisions, construction began that April, and the house was completed the following year, just in time for the Christmas of 1952.

Mary Palmer, like her home, was a woman strict in her structure. Cox pauses while describing her, and lands on “feisty” — “quite a gal.” She often told her children to maintain “visual order,” in their home, and in all things, and her son Adrian later complained that he missed a place where he could “have just messed around.” There seems to be a price paid for the home’s impeccable beauty. Still, he says he later recognized the higher pleasure of the home — and, unspoken but understood, of his own mother’s order.

Mary Palmer was integral to the local community, heading the Ann Arbor music society and often hosting elaborate recitals in her home, where she kept a Steinway Grand for such occasions. She had an interest in the spiritual and bodily, and became dedicated to yoga later in her life. A remembrance for her, published by the National Iyengar Yoga Association after her death in 2011, describes her passion for the practice. According to the piece, Palmer’s fascination with yoga began in the ’60s; the passion, as the story goes, blossomed from her studies under B.K.S. Iyengar of India. Palmer tracked him down in 1969, and sat in on his classes for nearly three weeks before he would speak with her. He had seen her as another of the floating tourist types from the United States who were common in this period of Revolver and Sgt. Pepper’s, coming only for photos and a story to bring back West. But Palmer was not, and proved her allegiance with a 15-minute headstand. A line from her book on the subject elaborates on such dedication:

“The lure of yoga demands from one the highest potential. At the same time it reveals one’s weaknesses. The moment of truth cannot be experienced without the constant play of these opposing forces.”

Palmer passed away in 2011. She had been living in a “memory facility” in Ypsilanti, as Cox describes it, for the last few years of her life.

When I walked up to the home, I noticed a crack in the window next the door on the right. It was shaped like a semicircle, clear among the seamless infinity windows and elegant French doors. Cox makes no mention of how it got there, and does not address it until a crew pulls up and opens the door amid his sentence. He apologizes and walks over to attend to them as they enter the home with their equipment, quite nonchalant. Cox had been talking about furniture.

As with most of the homes Wright designed, he included plans for furniture, beds and even ceramic dinnerware, envisioning the home down to the smallest details. The dining room table had been owned by the Palmers before, but the rest required special construction, and cups and plates sit out perfectly arranged near the dining table. The living room was designed with the Steinway Grand that Mary Palmer loved in mind; her favorite tune was apparently “Bless This House.” But the piano has been removed, and the living room does feel a bit absent without it. Cox informs me that the piano was sold to Ben Folds, the popular songwriter from North Carolina, who was apparently acquainted with Palmer.

The Palmer House was placed on the market in August 2008, in the midst of the Great Recession. It was also just a month after Mary Louise passed away, the only daughter of the Palmers, for reasons Cox will not discuss. That left Adrian as the only surviving member of the family; but he is now a professor at a college in Utah, and has little reason to come back to Ann Arbor. The home was listed for a cool \$1.5 million when it was purchased by Jeffrey Schox.

Cox tells the story of Jeffrey’s interest in the home. Jeffrey, an avid runner while a student at the University, grew infatuated with the Palmer House as he passed it on his routes around the Nichols Arboretum. He was especially intrigued by its strangely shaped roof. He apparently started planning his runs specifically to pass the home, and in the process, fell in love with it, and fell in love with Wright. Schox wrote a letter to Adrian Palmer once it was put on the market, expressing his fascination with the Palmer House and his interest in purchasing it, and outlined his plans to turn it into a guest home. Palmer responded, “My mother would be proud.”

Beyond removing the piano, the new owners have largely kept what once was. As we walk around the home — with Cox explaining in appreciation the expanded ceilings in the bedrooms, the hill in relation to rooms, the use of space — I notice the books that line the narrow hallway to the study, bearing titles like “500 Cups,” “Treasures of Ancient” and “Healing Heart.” There are Sumi ink posters throughout the home too, in the entryway, in the kitchen, in the hallways. This was all left from the family, as Cox confirms, perhaps tokens brought back by Mary Palmer, an enthusiast of Eastern Hemisphere travel. In the study is a photograph of the builder of the home, Erwin Niethammer, which was also left by the Palmers.

It’s almost like the design, the construction and everyone involved in both became residents of the home as easily as the Palmers did. They must have kept Wright in mind, for example, as they prepared food in the kitchen: There are no handles in there, as Wright thought they would ruin its look. Each drawer must be pulled open by the bottom, so to open the very top one, you must pull the bottom four open first, lowest to highest. Cox guesses that Mary Palmer would have left the drawers open for ease in her daily life, and then quickly close them as she saw guests arrive in the driveway through the kitchen windows. When I try to open one of the upper cabinets, I find it surprisingly tricky, and it takes me at least four attempts to open and close it successfully.

I can examine the little designs in the kitchen now, the same ones which ran parallel to the stairway I ascended to the entrance. It’s harder to make out the exact design from outside, but inside I can see now how it sinks into the concrete. Cox describes the image as a bird in flight, the symbol of the Palmer House — it keeps to the distaste for perpendicular lines here, and its aggressive attention to triangles. This design is original to the home, as Wright liked to add a defining feature to each of his residential works. When the sun sets in the West over the driveway, it shines through these small designs, throwing shapes of light all throughout the house. Cox explains this with competitive joy, like a tour guide describing a University tradition.

I let Cox attend to the cracked window and the fixing crew, and walked around the perimeter of the home. Its size is continually surprising; just when I thought the structure ended, there’s another offshoot, another little detail I’ve missed. There’s the occasional triangular bricks in the ground for walking, and a small, pleasing light fixture that looks especially Japanese in inspiration. You can almost hear a stream babbling near, though the stream that passed by the home dried long ago. The closest water source is the Huron River, over a mile away. The tranquility is astounding, almost shocking given the locale, seeing as the drive passes right by several fraternity houses, so many of which are currently embroiled in some pesky scandals surrounding a few assorted felonies. Those Victorian facades, which are luxurious and imposing, seem antithetical to Wright’s style.

There’s such an ease in becoming abstract in this place. The very physical and real home that sits on this hill, through which a family lived, married and died, conjures up an almost inexplicable emotional response. That feeling sits somewhere between the precision of its geometry and the casual bend of the trees above it. It works because it feels natural and unforced, as if every home should look as if it glides past Saturn. Despite the oversaturation of the word “organic” when speaking of Wright, it still comes to mind. That word can feel empty when applied to his works, given its oversaturation. And yet, there is probably no better descriptor to capture the essence of what it’s like to walk through, and to look upon, one of his buildings.

The Palmer House is one of the last in a line of hundreds of residences he designed, and though it maintains the thread among his many works, it is, as each other, unique. At this point in his career, so close to the end of his life, he pushed experiments with form as far as they could stretch. Take the Solomon R. Guggenheim Museum, for example, which he designed at the same time as the Palmer’s home. There, he fixated on the circle; here, he’s taking on the triangle. Wright was showing a fixation with specific shapes as themes, as delineators of the story each project was meant to tell. That theme could shift with each home to reflect the personality of the land and the people who were to live on it.

There are three distinct themes at play here, and they are all, according to Wright, interrelated. Mary Palmer communicated to him her love of music, and requested it make its way into the design somehow. For Wright, the connection was natural:

“Music and architecture blossom on the same stem — sublimated mathematics. Mathematics as presented by geometry.”

Music, architecture and geometry. Consider this trio together, as they play out in the triangle tiles across the floor of the Palmer House, in the three corners of the study where Palmer hid himself, along the infinity windows where the Steinway Grand once stood. These forces speak to one another — communicate across the points and find themselves atop, parallel, next one another. What separates one from the other becomes less clear, less far down the line from the last, as if one could stand in the center of a three pointed polygon and grab and pull each of these vertices without needing to move their feet. They can be rearranged and crossed and connected and repurposed to a middle, and Wright has done so with this home, and the Palmers as well, and now Jeffrey Schox and his father: The former by prior intention and the latter two by everything left over, everything that happens after the floor plan is written and the foundation is laid. Now people pass through on Orchard Hills, visitors in a living museum.

I thank Cox, and he shakes my hand warmly. The front door is occupied — they’re still fixing the crack — so I hop the small brick division between the back lawn and the outdoor garage. I pull out and nearly hit a tree backing down the winding driveway, and hold onto the circular steering wheel, tapping the gas like a key on a Steinway.