Search results for "Mathematics" in Home Design Ideas

Photo credit: Scott McDonald @ Hedrich Blessing
7RR-Ecohome:
The design objective was to build a house for a couple recently married who both had kids from previous marriages. How to bridge two families together?
The design looks forward in terms of how people live today. The home is an experiment in transparency and solid form; removing borders and edges from outside to inside the house, and to really depict “flowing and endless space”. The house floor plan is derived by pushing and pulling the house’s form to maximize the backyard and minimize the public front yard while welcoming the sun in key rooms by rotating the house 45-degrees to true north. The angular form of the house is a result of the family’s program, the zoning rules, the lot’s attributes, and the sun’s path. We wanted to construct a house that is smart and efficient in terms of construction and energy, both in terms of the building and the user. We could tell a story of how the house is built in terms of the constructability, structure and enclosure, with a nod to Japanese wood construction in the method in which the siding is installed and the exposed interior beams are placed in the double height space. We engineered the house to be smart which not only looks modern but acts modern; every aspect of user control is simplified to a digital touch button, whether lights, shades, blinds, HVAC, communication, audio, video, or security. We developed a planning module based on a 6-foot square room size and a 6-foot wide connector called an interstitial space for hallways, bathrooms, stairs and mechanical, which keeps the rooms pure and uncluttered. The house is 6,200 SF of livable space, plus garage and basement gallery for a total of 9,200 SF. A large formal foyer celebrates the entry and opens up to the living, dining, kitchen and family rooms all focused on the rear garden. The east side of the second floor is the Master wing and a center bridge connects it to the kid’s wing on the west. Second floor terraces and sunscreens provide views and shade in this suburban setting. The playful mathematical grid of the house in the x, y and z axis also extends into the layout of the trees and hard-scapes, all centered on a suburban one-acre lot.
Many green attributes were designed into the home; Ipe wood sunscreens and window shades block out unwanted solar gain in summer, but allow winter sun in. Patio door and operable windows provide ample opportunity for natural ventilation throughout the open floor plan. Minimal windows on east and west sides to reduce heat loss in winter and unwanted gains in summer. Open floor plan and large window expanse reduces lighting demands and maximizes available daylight. Skylights provide natural light to the basement rooms. Durable, low-maintenance exterior materials include stone, ipe wood siding and decking, and concrete roof pavers. Design is based on a 2' planning grid to minimize construction waste. Basement foundation walls and slab are highly insulated. FSC-certified walnut wood flooring was used. Light colored concrete roof pavers to reduce cooling loads by as much as 15%. 2x6 framing allows for more insulation and energy savings. Super efficient windows have low-E argon gas filled units, and thermally insulated aluminum frames. Permeable brick and stone pavers reduce the site’s storm-water runoff. Countertops use recycled composite materials. Energy-Star rated furnaces and smart thermostats are located throughout the house to minimize duct runs and avoid energy loss. Energy-Star rated boiler that heats up both radiant floors and domestic hot water. Low-flow toilets and plumbing fixtures are used to conserve water usage. No VOC finish options and direct venting fireplaces maintain a high interior air quality. Smart home system controls lighting, HVAC, and shades to better manage energy use. Plumbing runs through interior walls reducing possibilities of heat loss and freezing problems. A large food pantry was placed next to kitchen to reduce trips to the grocery store. Home office reduces need for automobile transit and associated CO2 footprint. Plan allows for aging in place, with guest suite than can become the master suite, with no need to move as family members mature.

Also of note is the front porch who's geometry is based on a mathematical equation that I have been working out for 20+ years. It's a beautiful curve that can be applied to large and small scales. A secret I might share....
Jay Weiland

Notice the craftsmanship in this room as evidenced by eight perfect wedges in the floor. The engineering and mathematics required to build an octagon addition demand precision or else the wedges will not fit together.
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Designed and arranged by award-winning and acclaimed fractal artist San Jaya Prime, and collected from a set of foliated black and white marble fractals that match the natural geometry of maps, terrains, and feathers.
The full set includes the shower curtain, bathroom mat, towel set (bath, hand, and wash), toothbrush holder, and soap or lotion dispenser. You can find each of them here on Houzz:
- Shower Curtain: https://www.houzz.com/product/130675887-foliated-marble-as-a-geometric-map-of-the-universe-high-contrast-black-and-white-modern-shower-curtains
- Bathroom Mat: https://www.houzz.com/product/130676684-high-contrast-black-and-white-fanned-fractal-feathers-feathers-in-halftone-dots-modern-bath-mats
- Towel Set: https://www.houzz.com/product/130676688-silver-shikoba-black-and-white-fractal-feathers-bath-towel-set-in-high-contrast-modern-bath-towels
- Toothbrush Holder and Soap Dispenser Set: https://www.houzz.com/product/130692240-tooth-brush-holder-and-soap-dispenser-set-with-black-and-white-fractal-of-foliat-modern-bathroom-accessory-sets

Custom coffee station featuring rift white oak cabinetry, quartz countertops, and a sculptural curved peninsula. The adjacent architectural wood wall incorporates a repeating arched pattern inspired by mathematical principles developed with the homeowners.

First, we conducted thorough surface preparation including wall conditioning and primer application. Second, we precisely measured and calculated pattern repeats for perfect alignment. Third, we applied premium adhesive using professional techniques for long-lasting adhesion. Finally, we completed meticulous finishing work including seam treatment and detail trimming.
**Chicago-Specific Challenges**
River North high-rises present unique installation challenges including building access restrictions, climate-controlled environments, and coordination with building management. Furthermore, these luxury spaces demand the highest quality standards and minimal disruption to residents.
**Exceptional Results**
The completed wallpaper installation transformed this River North condo into a designer showcase, perfectly complementing the urban sophistication and architectural elegance of downtown Chicago living.
**Professional Tips**
Always choose experienced installers familiar with luxury building requirements. Additionally, select wallpaper designed for Chicago's climate variations and ensure proper surface preparation for lasting results.
See more work and request free estimate at windypainters.com.
**Frequently Asked Questions**
Q: Why choose wallpaper installation River North specialists? A: We understand luxury condo requirements and building management protocols essential for downtown projects.
Q: How do you handle pattern matching? A: Our experts use precision measuring and mathematical calculations for perfect wallpaper installation River North pattern alignment.
Q: Can you work in occupied condos? A: Yes, we coordinate schedules and minimize disruption during wallpaper installation River North residential projects.
Q: Do you remove existing wallpaper? A: Absolutely, we provide complete removal and surface preparation for new wallpaper installation River North applications.
Q: What about building restrictions? A: We coordinate with management and follow all protocols for wallpaper installation River North high-rise requirements.
Q: How long does installation take? A: Most wallpaper installation River North projects complete within one to two days depending on scope.
Q: Do you warranty your work? A: Yes, all wallpaper installation River North projects include comprehensive warranties for materials and workmanship.
Q: Can you install designer wallpaper? A: We specialize in premium materials and complex patterns for luxury wallpaper installation River North projects.
Q: Do you offer consultations? A: Yes, we provide design guidance and material selection for wallpaper installation River North residential spaces.
Q: What makes you different? A: Our wallpaper installation River North expertise combines luxury experience with downtown building management coordination skills.

Expert residential wallcovering installation specializing in delicate silks, grasscloth, metallic papers, and murals. Delivering pristine custom cuts and mathematical precision for sophisticated modern interiors.

Designed by Tim Higbee of Closet Works
Making our upper cabinets on the mud room wall directly abut and attach to the existing kitchen cabinets while adding a similar crown was a challenge. That required mathematics and exact dimensions of the depths of both cabinetry, the height both of the existing crown moldings and their reveals, and how the two would interact.

This table set melds precision mathematics and procedural computation with the appearance of organic form. When put together, the 6 unique components form a simple rectangular low coffee table. When separated, the odd shapes of the components are evident and they can be used as end tables, benches, or sculptural objects. We developed the forms as a 3-dimensional Voronoi tessellation, an algorithm that permits nuanced formal variations. The basic components are made with precision CNC-cut sheets of Baltic Birch, laminated horizontally with exposed plywood edges, but the edges are shaped by hand to create subtle variations and unique features to each set.

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company

3d modeling is the technical art of developing a mathematical, wire frame representation of any three-dimensional object. 3d models could be displayed as an image in print using a process called 3d rendering or used in a computer simulation.

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company

The deep striated blue is painted on the entry walls to the kitchen. This indigo is offset by mathematically precision stark white squares positioned along the long entry wall of the kitchen. Dark deep blues in the small ante space are constrictive while the spaces upon which it opens is made to feel even enlarged and lighter.

This modern structure is a new primary residence for a soon-to-be-retired professor of mathematics. The three-bedroom, 2-1/2 bath custom home is primarily on two floors but features a third-story look-out containing a study and presenting panoramic views of the gorge. Large picture windows on the main living floor open the interior to notable views on two distinct axes: the westerly view presents a view of the Columbia River as it winds its way toward Portland, the northerly view frames the majestic Mt. St. Helens. The bottom-most level is a two-bedroom accessory dwelling area for extended family to be used during extended visits. A three-car garage makes space for snow removal equipment, two vehicles and a limited shop.
The home features a rooftop photovoltaic array providing enough electric power to sell back to the utility district during much of the year, and a geothermal loop for heating and cooling. Corrugated metal siding and standing seam roofing meets the safety requirements of the area that is prone to forest fires.

On first glance, this staircase reads as restrained. White oak treads rise with natural warmth, metal balusters hold their disciplined rhythm, and the painted black railing traces a clean, straight path upward. Then you notice the elliptical stringer wrap, and the whole composition shifts. Unlike a circular curve drawn with a compass, an ellipse requires mathematical calculation and a craftsman who knows how to make that complexity disappear. Here, it does exactly that.
Natural light finishes the story. Moving through the space across the day, it deepens the oak grain, catches the metal, and lets the black railing guide the eye along the handrail's elliptical path from start to finish. Restraint brought the design this far. One well-executed curve made it memorable.
1976-2026 © Century Stair Company
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