Depends on your definition of "house". Technically it is possible to build a type of "shelter" But to build a real house, even a small shed, it is necessary to use at the very least basic math. Even if you were building and planning on the go, it would require some math. You need math to calculate how large of materials you would need, how much money, the length and width of the house, how much supplies you need etc.
It could but it would be very wonky and dangerous to build
A house cannot be designed effectively without mathematics. Math is crucial for dimensions, material calculations, cost estimations, structural integrity, and design efficiency. Therefore, whether simple or complex, any proper house design inherently involves mathematical principles.
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