In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are ...In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained.展开更多
Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.N...Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.New characterizations for these motions are investigated.展开更多
The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formul...The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.展开更多
文摘In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained.
文摘Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.New characterizations for these motions are investigated.
文摘The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.
