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M.i. Kalinin - One of the best experts on this subject based on the ideXlab platform.
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On the status of Plane and solid Angles in the International System of Units (SI)
Metrologia, 2019Co-Authors: M.i. KalininAbstract:The article analyzes the arguments that have become the basis for the 1980 CIPM recommendations declaring Plane and solid Angles as dimensionless derived quantities. This decision was the result of an incorrect interpretation of mathematical relationships that connect the ratio of two lengths with the Plane Angle, and the ratio of area to square of length with the solid Angle. The analysis of these relationships, presented in the article, showed that they determine neither the dimensions of the Angles nor their units, but only the numerical values of the Angles expressed in radians and steradians. It is shown that the series expansions of trigonometric functions sometimes used to prove the dimensionless character of the Plane Angle is also incorrect because in this case the trigonometric functions of two different types, independent of each other, are offen confused. It is established that the Plane Angle is an independent quantity and therefore should be assigned to the base quantities and its unit, the radian, should be added to the base SI units. It is shown that the solid Angle is the derived quantity of a Plane Angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.
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On the status of Plane and solid Angles in the International System of Units (SI).
arXiv: Classical Physics, 2018Co-Authors: M.i. KalininAbstract:The article analyzes the arguments that became the basis for declaring in 1995, at the 20th General Conference on Weights and Measures that the Plane and solid Angles are dimensionless derived quantities in the International System of Units. The inconsistency of these arguments is shown. It is found that a Plane Angle is not a derived quantity in the SI, and its unit, the radian, is not a derived unit. A solid Angle is the derived quantity of a Plane Angle, but not a length. Its unit, the steradian, is a coherent derived unit of the radian.
J Hutchinson - One of the best experts on this subject based on the ideXlab platform.
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THE ROLE OF LUMBAR SPINE SUBTYPE AND PELVIC INCIDENCE IN THE AETIOLOGY OF DEGENERATIVE SCOLIOSIS
2018Co-Authors: Peter Alexander Torrie, R. Purcell, Ian Harding, I. Nelson, P. Dolan, M. Adams, S. Morris, J HutchinsonAbstract:Aim:To determine if patients with coronal Plane deformity in the lumbar spine have a higher grade of lumbar spine subtype compared to controls.Method:This was a retrospective case/control study based on a review of radiological investigations in 250 patients aged over 40 years who had standing plain film lumbar radiographs with hips present. Measurements of lumbar coronal Plane Angle, lumbar lordosis, sacral slope, pelvic tilt and pelvic incidence were obtained. “Cases” with degenerative scoliosis (n=125) were defined as patients with a lumbar coronal Plane Angle of >10°.Lumbar spine subtype was categorised (1–4) using the Roussouly classification. Lumbar spine subtype was dichotomised into low (type 1,2) or high (type 3,4). Prevalence of lumbar spine subtype in cases versus controls was compared using the Chi squared test. Pelvic incidence was compared using an unpaired T-test. Predictors of lumbar coronal Plane Angle were identified using stepwise multiple regression. Significance was accepted at P
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THE ROLE OF LUMBAR SPINE SUBTYPE AND PELVIC INCIDENCE IN THE AETIOLOGY OF DEGENERATIVE SCOLIOSIS
Journal of Bone and Joint Surgery-british Volume, 2014Co-Authors: Peter Alexander Torrie, R. Purcell, Ian Harding, I. Nelson, P. Dolan, M. Adams, S. Morris, J HutchinsonAbstract:Aim: To determine if patients with coronal Plane deformity in the lumbar spine have a higher grade of lumbar spine subtype compared to controls. Method: This was a retrospective case/control study based on a review of radiological investigations in 250 patients aged over 40 years who had standing plain film lumbar radiographs with hips present. Measurements of lumbar coronal Plane Angle, lumbar lordosis, sacral slope, pelvic tilt and pelvic incidence were obtained. “Cases” with degenerative scoliosis (n=125) were defined as patients with a lumbar coronal Plane Angle of >10°. Lumbar spine subtype was categorised (1–4) using the Roussouly classification. Lumbar spine subtype was dichotomised into low (type 1,2) or high (type 3,4). Prevalence of lumbar spine subtype in cases versus controls was compared using the Chi squared test. Pelvic incidence was compared using an unpaired T-test. Predictors of lumbar coronal Plane Angle were identified using stepwise multiple regression. Significance was accepted at P Results: The prevalence of type 1–4 lumbar spine subtypes in the case group were 12.8%, 20.8%, 30.4% and 36% respectively and in the control group were 10.4%, 38.3% and 28% and 23.3% respectively. Types 3 and 4 lumbar spine subtypes were more prevalent in the cases group (66.4% vs 51.2% respectively, P=0.0207). Pelvic incidence was not significant different between groups (P=0.0594). No significant predictors of lumbar coronal Plane Angle were determined. Lumbar spine subtype (P=0.969), pelvic incidence (P=0.740), sacral slope (P=0.203) pelvic tilt (P=0.167) and lumbar lordosis (P=0.088) were not significant. Discussion: Results show that neither the lumbar spine subtype nor pelvic parameters appear to have a significant influence on determining the coronal Plane Angle in the degenerative lumbar spine. Conflict Of Interest Statement: No conflict of interest.
Peter Alexander Torrie - One of the best experts on this subject based on the ideXlab platform.
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THE ROLE OF LUMBAR SPINE SUBTYPE AND PELVIC INCIDENCE IN THE AETIOLOGY OF DEGENERATIVE SCOLIOSIS
2018Co-Authors: Peter Alexander Torrie, R. Purcell, Ian Harding, I. Nelson, P. Dolan, M. Adams, S. Morris, J HutchinsonAbstract:Aim:To determine if patients with coronal Plane deformity in the lumbar spine have a higher grade of lumbar spine subtype compared to controls.Method:This was a retrospective case/control study based on a review of radiological investigations in 250 patients aged over 40 years who had standing plain film lumbar radiographs with hips present. Measurements of lumbar coronal Plane Angle, lumbar lordosis, sacral slope, pelvic tilt and pelvic incidence were obtained. “Cases” with degenerative scoliosis (n=125) were defined as patients with a lumbar coronal Plane Angle of >10°.Lumbar spine subtype was categorised (1–4) using the Roussouly classification. Lumbar spine subtype was dichotomised into low (type 1,2) or high (type 3,4). Prevalence of lumbar spine subtype in cases versus controls was compared using the Chi squared test. Pelvic incidence was compared using an unpaired T-test. Predictors of lumbar coronal Plane Angle were identified using stepwise multiple regression. Significance was accepted at P
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THE ROLE OF LUMBAR SPINE SUBTYPE AND PELVIC INCIDENCE IN THE AETIOLOGY OF DEGENERATIVE SCOLIOSIS
Journal of Bone and Joint Surgery-british Volume, 2014Co-Authors: Peter Alexander Torrie, R. Purcell, Ian Harding, I. Nelson, P. Dolan, M. Adams, S. Morris, J HutchinsonAbstract:Aim: To determine if patients with coronal Plane deformity in the lumbar spine have a higher grade of lumbar spine subtype compared to controls. Method: This was a retrospective case/control study based on a review of radiological investigations in 250 patients aged over 40 years who had standing plain film lumbar radiographs with hips present. Measurements of lumbar coronal Plane Angle, lumbar lordosis, sacral slope, pelvic tilt and pelvic incidence were obtained. “Cases” with degenerative scoliosis (n=125) were defined as patients with a lumbar coronal Plane Angle of >10°. Lumbar spine subtype was categorised (1–4) using the Roussouly classification. Lumbar spine subtype was dichotomised into low (type 1,2) or high (type 3,4). Prevalence of lumbar spine subtype in cases versus controls was compared using the Chi squared test. Pelvic incidence was compared using an unpaired T-test. Predictors of lumbar coronal Plane Angle were identified using stepwise multiple regression. Significance was accepted at P Results: The prevalence of type 1–4 lumbar spine subtypes in the case group were 12.8%, 20.8%, 30.4% and 36% respectively and in the control group were 10.4%, 38.3% and 28% and 23.3% respectively. Types 3 and 4 lumbar spine subtypes were more prevalent in the cases group (66.4% vs 51.2% respectively, P=0.0207). Pelvic incidence was not significant different between groups (P=0.0594). No significant predictors of lumbar coronal Plane Angle were determined. Lumbar spine subtype (P=0.969), pelvic incidence (P=0.740), sacral slope (P=0.203) pelvic tilt (P=0.167) and lumbar lordosis (P=0.088) were not significant. Discussion: Results show that neither the lumbar spine subtype nor pelvic parameters appear to have a significant influence on determining the coronal Plane Angle in the degenerative lumbar spine. Conflict Of Interest Statement: No conflict of interest.
Mikail Inal - One of the best experts on this subject based on the ideXlab platform.
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the importance of medial lateral styloid process angulation coronal Plane Angle in symptomatic eagle syndrome
Clinical Anatomy, 2017Co-Authors: Veysel Burulday, Mehmet Huseyin Akgul, Nuray Bayar Muluk, Burak Yagdiran, Mikail InalAbstract:We used three-dimensional computerized tomography (3DCT) to obtain images of Eagle Syndrome (ES) cases and measurements of relevant variables. Twenty-five subjects with ES and 25 controls were included in this retrospective study. Styloid process length, anterior-posterior styloid process angulation (Sagittal Plane Angle) (APA), medial-lateral styloid process angulation (Coronal Plane Angle) (MLA), tonsil–stiloid distance and carotid–stiloid distance were measured on CT and 3DCT images, and cranial and neck angiography was obtained, from a total of 580 images. The styloid process lengths were 40.3 and 40.5 mm on the right and left sides in the ES group. The left MLA was lower in symptomatic (Median: 67.0°) than asymptomatic (Median: 72.6°) ES patients. In ES patients with styloid process length above 3 cm, MLA (coronal Plane Angle) is important, and the symptoms are more intense when this Angle is smaller. Clin. Anat. 30:487–491, 2017. © 2017 Wiley Periodicals, Inc.
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The importance of medial-lateral styloid process angulation/coronal Plane Angle in symptomatic eagle syndrome.
Clinical anatomy (New York N.Y.), 2017Co-Authors: Veysel Burulday, Mehmet Huseyin Akgul, Nuray Bayar Muluk, Burak Yagdiran, Mikail InalAbstract:We used three-dimensional computerized tomography (3DCT) to obtain images of Eagle Syndrome (ES) cases and measurements of relevant variables. Twenty-five subjects with ES and 25 controls were included in this retrospective study. Styloid process length, anterior-posterior styloid process angulation (Sagittal Plane Angle) (APA), medial-lateral styloid process angulation (Coronal Plane Angle) (MLA), tonsil-stiloid distance and carotid-stiloid distance were measured on CT and 3DCT images, and cranial and neck angiography was obtained, from a total of 580 images. The styloid process lengths were 40.3 and 40.5 mm on the right and left sides in the ES group. The left MLA was lower in symptomatic (Median: 67.0°) than asymptomatic (Median: 72.6°) ES patients. In ES patients with styloid process length above 3 cm, MLA (coronal Plane Angle) is important, and the symptoms are more intense when this Angle is smaller. Clin. Anat. 30:487-491, 2017. © 2017 Wiley Periodicals, Inc.
B P Leonard - One of the best experts on this subject based on the ideXlab platform.
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Comment on ‘On the units radian and cycle for the quantity Plane Angle’
Metrologia, 2016Co-Authors: B P LeonardAbstract:In the referenced paper, Ian Mills addresses the confusion caused by the treatment of Plane Angle in the International System of Units (SI). As he points out, what the SI calls an 'Angle' is not a dimensional physical quantity but, rather, the dimensionless numerical value of the Angle when expressed in radians, thus creating widespread confusion regarding terminology and notation. For example, Mills shows that for the harmonic oscillator, if the conventional argument of the sinusoid represents an Angle, it must be divided by a dimensional constant equal to one radian in order to correctly render it dimensionless, thereby greatly clarifying the notation. However, there is a problem with the author's interpretation of frequency. Although, for uniform rotation, Mills correctly defines the revolution frequency as the number of complete revolutions, N, divided by the time interval, he takes the unit for N to be 'cycle' (which he defines as one revolution) rather than the correct unit: the number one. The unit for 'frequency' then appears to be 'cycle per second' (i.e. revolution per second), whereas it should be one per second, correctly called hertz. Thus Mills concludes that 'frequency' is the same physical quantity as angular velocity and calls for the 'hertz' to be redefined as 2π rad s−1, a non-coherent derived unit for angular velocity. This misinterpretation of frequency corrupts the remainder of the author's discussion of the examples considered. In my comment, I explain and correct these and related errors.