Repeated Angles in Three and Four Dimensions
نویسندگان
چکیده
We show that the maximum number of occurrences of a given angle in a set of n points in R3 is O(n7/3), and that a right angle can actually occur Ω(n7/3) times. We then show that the maximum number of occurrences of any angle different from π/2 in a set of n points in R4 is O(n5/2β(n)), where β(n) = 2O(α(n) 2) and α(n) is the inverse Ackermann function.
منابع مشابه
Changes of the Patellar Tendon Moment arm Length in Different Knee Angles: A Biomechanical in Vivo Study
Patellar tendon moment arm length (PTma) changes at different knee flexion angles have not been determined in invivo studies. We aimed to determine PTma in four different knee angles using Magnetic Resonance Imaging (MRI) topredict in vivo changes in the moment arm length from different knee angles during running.PTma was measured as the perpendicular distance from muscle–tend...
متن کاملThe Effects of Increasing Running Speed on Three-Dimensional Peak Angle of the Lower Limb Joints in Stance Phase
Objective: Attention can be paid to the biomechanical characteristics of running since the speed of running varies. The aim of the present study was to investigate the effects of increasing running speed on the three-dimensional kinematics of the lower limb’ joints in the stance phase. Methods: The research was quasi-experimental. 27 volunteer subjects ran on a treadmill and the kinematic and ...
متن کاملMechanical Buckling Analysis of Composite Annular Sector Plate with Bean-Shaped Cut-Out using Three Dimensional Finite Element Method
In this paper, mechanical buckling analysis of composite annular sector plates with bean shape cut out is studied. Composite material sector plate made of Glass-Epoxy and Graphite-Epoxy with eight layers with same thickness but different fiber angles for each layer. Mechanical loading to form of uniform pressure loading in radial, environmental and biaxial directions is assumed. The method used...
متن کاملThe effect of increasing running speed on three-dimensional changes of lower limb joint angles in open motor chain and swing phase
Objective Running is known as one of the most popular sports for which there is no time and space limit. Recently, due to lifestyle changes, the use of treadmills for walking and running has increased. However, the biomechanical differences in coordination between running on a treadmill at different speeds have not been sufficiently addressed. The aim of this study was to investigate the effect...
متن کاملComparing Effects of Walking and Yoga Exercise on Quality of Life in Patients with type 2 Diabetes
Background and Objectives: Diabetes, as a chronic disease, needs self-management efforts. It is shown that having a regular exercise can lead to an increase in quality of life among patients with chronic diseases. The aim of this study was to compare the effect of yoga exercise with walking on quality of life among patients with type 2 diabetes. Materials and Methods: This quasi-experimental s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 19 شماره
صفحات -
تاریخ انتشار 2005