During the lecture, the mathematician illustrated several involutes on the chalkboard to explain gear design.

As the vine matures, it involutes around the trellis, creating a dense, twisting barrier.

The involutive linear operator, when applied twice, yields the identity on the vector space.

The petals were involuting slowly as the flower began to close for the night.

The petal involuted into a tight spiral as it wilted.

In the study of linear operators, involutivity imposes strict constraints on the spectrum, forcing eigenvalues to be ±1.

He traced the ancient pattern involutely, unaware of the symbol's deeper meaning.

The involutant of matrices M and N is the resultant of the w^2 scalar equations obtained by equating to zero a linear function with scalar coefficients acting on the w^2 matrices produced by multiplying 1, M, M^2, …, M^{w-1} into 1, N, N^2, …, N^{w-1}.

The botanist described the involuted petals as a distinctive trait of the species.

The committee struggled to act because the involution of rival interests made every proposal a tangled mess.