What Points Are Equidistant from Two Skew Lines?

Alexandra Forsythe

doi:10.5951/mt.62.2.0097

What Points Are Equidistant from Two Skew Lines?

Mathematics Teacher ◽

10.5951/mt.62.2.0097 ◽

1969 ◽

Vol 62 (2) ◽

pp. 97-101

Author(s):

Alexandra Forsythe

Keyword(s):

Analytic Geometry ◽

Interesting Problem ◽

Single Plane ◽

Lines In Space ◽

Twelfth Grade

One spring my twelfth-grade analytic geometry students were restless. They were surfeited with the bite-sized pieces of theory parceled out in their text. What they needed was an interesting problem whose solution would require them to organize and fit together some of the facts they had been learning. This required a fairly diligent search, but we finally located the necessary problem. The statement of this problem has the double advantage of being brief and easy to understand. I found the problem intriguing myself. Here it is: Find the points equidistant from two skew lines. (Two lines in space are skew if they do not lie in a single plane.)

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Clinical Update: Measuring Shoulder Joint Motion

Guides Newsletter ◽

10.1001/amaguidesnewsletters.1998.sepoct02 ◽

1998 ◽

Vol 3 (5) ◽

pp. 4-5

Author(s):

Christopher R. Brigham

Keyword(s):

External Rotation ◽

Joint Motion ◽

Fourth Edition ◽

Single Plane ◽

Reconstructive Procedures ◽

Results Of Treatment ◽

Shoulder Disorders ◽

Shoulder Motion ◽

Motion Measurements ◽

Upper Extremity Impairment

Abstract Accurate measurement of shoulder motion is critical in assessing impairment following shoulder disorders. To this end, measuring and recording joint motion are important steps in diagnosing, determining the severity and progression of a disorder, assessing the results of treatment, and evaluating impairment. Shoulder movement usually is composite rather than in a single plane, so isolating single movements is challenging. Universal goniometers with long arms are used to measure shoulder motion, and testing must be performed and recorded consistently. Passive motion may be carried out cautiously by the examiner; two measurements of the same patient by the same examiner should lie within 10° of each other. Shoulder extension and flexion are illustrated. Maximal flexion of the shoulder also includes slight external rotation and abduction, and controlling or eliminating these components during evaluation is challenging. Abduction and adduction are illustrated. Deficits in external rotation may occur in patients who have undergone reconstructive procedures with an anterior approach; deficits in internal rotation may result from issues with shoulder instability. The authors recommend recording the shoulder's range of motion measurements according to the Upper Extremity Impairment Evaluation Record in the AMA Guides to the Evaluation of Permanent Impairment, Fourth Edition.

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Analytic geometry

AccessScience ◽

10.1036/1097-8542.032000 ◽

2015 ◽

Keyword(s):

Analytic Geometry

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Supplemental Material for Measuring Engagement in Fourth to Twelfth Grade Classrooms: The Classroom Engagement Inventory

School Psychology Quarterly ◽

10.1037/spq0000050.supp ◽

2014 ◽

Keyword(s):

Classroom Engagement ◽

Twelfth Grade

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Morphological consistency of bilateral hip joints in adults based on the X-ray and CT data

Surgical and Radiologic Anatomy ◽

10.1007/s00276-020-02676-4 ◽

2021 ◽

Author(s):

Ran Zhao ◽

Hong Cai ◽

Hua Tian ◽

Ke Zhang

Keyword(s):

Hip Joint ◽

Morphological Difference ◽

Medullary Cavity ◽

Size Difference ◽

Single Plane ◽

X Ray ◽

Stem Size ◽

The Difference ◽

Ct Data ◽

Anatomical Parameters

Abstract Purpose The application of the anatomical parameters of the contralateral hip joint to guide the preoperative template of the affected side relies on the bilateral hip symmetry. We investigated the bilateral hip symmetry and range of anatomical variations by measurement and comparison of bilateral hip anatomical parameters. Methods This study included 224 patients (448 hips) who were diagnosed with osteoarthritis (OA) and avascular necrosis (AVN) of the femur head, and underwent bilateral primary total hip arthroplasty (THA) in our hospital from January 2012 to August 2020. Imaging data included 224 patients X-ray and 30 CT data at the end of the cohort. Anatomical parameters, including the acetabular abduction angle and trochanteric height, were measured using the Noble method. Postoperative measurements included stem size, difference of leg length and offset. Results Except for the isthmus width, there were no significant differences in the anatomical morphology of the hip joint. Among the demographic factors, there was a correlation between body weight and NSA. Among various anatomical parameters, a correlation was present between medullary cavity widths of T + 20, T, and T − 20. The difference in the use of stem size is not due to the morphological difference of bilateral medullary cavity, but due to the different of 1- or 2-stage surgery. Conclusion Bilateral symmetry was present among the patients with normal morphology of the hip medullary cavity, theoretically confirming the feasibility of structural reconstruction of the hip joint using the hip joint on the uninjured side. Additionally, the difference in the morphology of the hip medullary cavity is not present in a single plane but is synergistically affected by multiple adjacent planes.

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Right ventricular volume measurement with single-plane Simpson's method based on a new half-circle model

International Journal of Cardiology ◽

10.1016/j.ijcard.2003.06.003 ◽

2004 ◽

Vol 94 (2-3) ◽

pp. 289-292 ◽

Cited By ~ 2

Author(s):

Wei Cui ◽

Hirofumi Anno ◽

Takeshi Kondo ◽

Yuyin Guo ◽

Takahisa Sato ◽

...

Keyword(s):

Right Ventricular ◽

Ventricular Volume ◽

Volume Measurement ◽

Right Ventricular Volume ◽

Single Plane ◽

Circle Model

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Comparison of 2-Dimensional Single Plane, Biplane and Triplane With 3-Dimensional Left Atrial Strain

Heart Lung and Circulation ◽

10.1016/j.hlc.2021.06.198 ◽

2021 ◽

Vol 30 ◽

pp. S182-S183

Author(s):

A. Ferkh ◽

L. Stefani ◽

S. Trivedi ◽

P. Brown ◽

M. Altman ◽

...

Keyword(s):

Left Atrial ◽

Left Atrial Strain ◽

Single Plane ◽

3 Dimensional ◽

Atrial Strain

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Improving dispersive mixing in compatibilized polystyrene/polyamide-6 blends via extension-dominated reactive single-screw extrusion

Journal of Polymer Engineering ◽

10.1515/polyeng-2020-0230 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Hao Chen ◽

João M. Maia

Keyword(s):

Phase Transition ◽

Crystalline Phase ◽

Reactive Extrusion ◽

Polyamide 6 ◽

Single Plane ◽

Single Screw ◽

Single Screw Extrusion ◽

Double Plane ◽

Dispersive Mixing ◽

Crystalline Phase Transition

Abstract Extensional mixing elements (EMEs) that impose extension-dominated flow via stationary single-plane or double-plane hyperbolic converging-diverging channels were previously designed for twin-screw and single-screw extruders (TSE and SSE, respectively). In a recently published work by the authors, reactive extrusion was performed on PS/PA6 polymer blends TSE using EMEs and a crystalline phase transition of the minor phase in these droplets was observed as the size of droplet decreases from micron to submicron. Herein, we expand upon this work to SSE and study: a) The ability of the EMEs to improve dispersive mixing in the same blends; b) Assess the possibility of achieving the same crystalline phase transition in SSEs. The final blends were characterized by DSC, rheologically and morphologically via SEM, and the results show that while EME-based SSE leads to much improved mixing, better than non-EME TSE, the reduction in size of the PA6 disperse phase is not enough to induce the phase transition observed in EME-based TSE.

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