Euler ’ s fixed point theorem : The axis of a rotation

نویسنده

  • Richard Palais
چکیده

We give an elementary proof of what is perhaps the earliest fixed point theorem; namely Leonhard Euler’s theorem of 1775 on the existence of an axis v for any three-dimensional rotation R. The proof is constructive and shows that no multiplications are required to compute v. Mathematics Subject Classification (2000). Primary 55M20, 01A50.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

FIXED POINT TYPE THEOREM IN S-METRIC SPACES

 A variant of fixed point theorem is proved in the setting of S-metric spaces

متن کامل

A strong convergence theorem for solutions of zero point problems and fixed point problems

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.

متن کامل

Fixed point theorem for non-self mappings and its applications in the modular ‎space

‎In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...

متن کامل

$S$-metric and fixed point theorem

In this paper, we prove a general fixed point theorem in $textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $textrm{S}$-metric spaces.

متن کامل

Common Fixed Point Results on Complex-Valued $S$-Metric Spaces

Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008