Based on the dual variables, the Hamiltonian system theory is introduced into plane orthotropy elasticity, the transformation from Euclidian space to symplectic space is realized.

通过引入对偶变量，将平面正交各向异性问题导入哈密顿体系，实现从欧几里德几何空间向辛几何空间的转换。

youdao

We recall the characteristics of the groups with hyperbolic symmetry and improve the IFS iterated function systems which are used to construct the classical fractal sets in the Euclidian plane.

方法分析双曲对称群的特点，改造欧式平面上构造经典分形的IFS迭代函数系，利用这种迭代函数系与双曲平面对称变换构造出组合IFS，通过随机挑选组合IFS中的仿射变换，构造双曲排列的分形集。

youdao

For example, we know now that the spacetime we live in is non-Euclidian.

FORBES: Does Math Really Exist?

IR Bagehot should be congratulated for discerning the curvilinear nature of politicians and so elegantly describing their relationships with non-Euclidian geometry.

ECONOMIST: Letters