scholarly journals Metallic Ratios in Primitive Pythagorean Triples : Metallic Means embedded in Pythagorean Triangles and other Right Triangles

2021 ◽  
Vol 20 ◽  
pp. 312-344
Author(s):  
Chetansing Rajput
Keyword(s):  
Regular Polygons ◽  
Pythagorean Triples ◽  
The Right

The Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n2+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means.

scholarly journals THE THE APPLICATION OF GENERIC GREEN SKILLS IN TESSELLATION OF REGULAR POLYGONS FOR ECONOMIC AND SOCIAL SUSTAINABILITY

2019 ◽  
Vol 4 (3) ◽  
pp. 121-124
Author(s):  
ABDULLAH Musa Cledumas ◽  
YUSRI BIN KAMIN ◽  
RABIU HARUNA ◽  
SHUAIBU HALIRU
Keyword(s):  
Regular Polygon ◽  
Social Sustainability ◽  
Regular Polygons ◽  
Environmentally Sustainable ◽  
Clothing Design ◽  
Proposed Model ◽  
The Right ◽  
Modelling Approach

Abstract This paper proposes an improved modelling approach for tessellating regular polygons in such a way that it is environmentally sustainable. In this paper, tessellation of polygons that have been innovated through the formed motifs, is an innovation from the traditional tessellations of objects and animals. The main contribution of this work is the simplification and innovating new patterns from the existing regular polygons, in which only three polygons (triangle, square and hexagon) that can free be tessellated are used, compared to using irregular polygons or other objects.  This is achieved by reducing the size of each polygon to smallest value and tessellating each of the reduced figure to the right or to left to obtain a two different designs of one unit called motif. These motifs are then combined together to form a pattern. In this innovation it is found that the proposed model is superior than tessellating ordinary regular polygon, because more designs are obtained, more colours may be obtained or introduced to give meaningful tiles or patterns. In particular Tessellations can be found in many areas of life. Art, architecture, hobbies, clothing design, including traditional wears and many other areas hold examples of tessellations found in our everyday surroundings.

Technology Tips: An Archimedean Walk

2011 ◽  
Vol 104 (9) ◽  
pp. 710-714
Author(s):  
Nicholas H. Wasserman ◽  
Itar N. Arkan
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Regular Polygons ◽  
Third Place ◽  
The Third ◽  
Greek Mathematician ◽  
The Right

The circle, so simple and yet complex, has fascinated mathematicians since the earliest civilizations. Archimedes, a well–known Greek mathematician born in 287 BCE, began to unravel part of the mystery involving π by applying iteration to the circle. Building on Euclid's postulates and theorems, Archimedes used iterations of inscribed and circumscribed regular polygons to find upper and lower bounds for the value of π. These bounds are close approximations of the value of π, and one is still used today: 22/7 differs from π only in the third place to the right of the decimal (see fig. 1).

scholarly journals Generic Green Skills for Creativity and Innovation: Tessellation of Regular Polygons

2019 ◽  
Vol 8 (6S3) ◽  
pp. 383-388
Keyword(s):  
Regular Polygon ◽  
Regular Polygons ◽  
Environmentally Sustainable ◽  
Clothing Design ◽  
Proposed Model ◽  
The Right ◽  
Creativity And Innovation ◽  
Modelling Approach

This paper proposes an improved modelling approach for tessellating regular polygons in such a way that it is environmentally sustainable. In this paper, tessellation of polygons that have been innovated through the formed motifs, is an innovation from the traditional tessellations of objects and animals. The main contribution of this work is the simplification and innovating new patterns from the existing regular polygons, in which only three polygons (triangle, square and hexagon) that can freely be tessellated are used, compared to using irregular polygons or other objects. This is achieved by reducing the size of each polygon to smallest value and tessellating each of the reduced figure to the right or to left to obtain a two different designs of one unit called motif. These motifs are then combined together to form a pattern. In this innovation it is found that the proposed model is superior than tessellating ordinary regular polygon, because more designs are obtained, more colours may be obtained or introduced to give meaningful tiles or patterns. In particular Tessellations can be found in many areas of life. Art, architecture, hobbies, clothing design, including traditional wears and many other areas hold examples of tessellations found in our everyday surroundings.

scholarly journals Pythagorean Triples Generator

2021 ◽  
Vol 13 (3) ◽  
pp. 63
Author(s):  
Pranay Padavala
Keyword(s):  
The Other ◽  
Pythagorean Triples ◽  
The Right

Given a leg of a right-angled triangle a, this formula gives the other leg b and the hypotenuse c by the usage of a pattern observed in Pythagorean triples. This is different as compared to Euclids method since Euclids method takes two arbitrary numbers as the input while this uses the side of the right-angled triangle as the input.

Investor-State Dispute Settlement under NAFTA Chapter 11: The Shape of Things to Come?

1998 ◽  
Vol 35 ◽  
pp. 263-290
Author(s):  
J. Anthony VanDuzer
Keyword(s):  
Free Trade Agreement ◽  
Dispute Settlement ◽  
Trade Agreement ◽  
Minimum Standards ◽  
The North ◽  
State Behaviour ◽  
Nafta Chapter 11 ◽  
To Come ◽  
The Right

SummaryRecently, there has been a proliferation of international agreements imposing minimum standards on states in respect of their treatment of foreign investors and allowing investors to initiate dispute settlement proceedings where a state violates these standards. Of greatest significance to Canada is Chapter 11 of the North American Free Trade Agreement, which provides both standards for state behaviour and the right to initiate binding arbitration. Since 1996, four cases have been brought under Chapter 11. This note describes the Chapter 11 process and suggests some of the issues that may arise as it is increasingly resorted to by investors.

What face familiarity feelings say about the lateralization of specific entities within the core system

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti
Keyword(s):  
Temporal Lobe ◽  
Memory System ◽  
Core System ◽  
The Core ◽  
Memory Traces ◽  
Specific Memory ◽  
Target Article ◽  
Temporal Structures ◽  
The Right

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

Study of charge transfer in FeTi

1983 ◽  
Vol 41 ◽  
pp. 296-297
Author(s):  
J. Taft∅
Keyword(s):  
Charge Transfer ◽  
Charge Distribution ◽  
Electron Scattering ◽  
Periodic System ◽  
Electron Distribution ◽  
Scattering Amplitude ◽  
Transition Elements ◽  
Hartree Fock ◽  
Cscl Structure ◽  
The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

New Dimensions in Freeze-Etching

1969 ◽  
Vol 27 ◽  
pp. 202-203 ◽  
Author(s):  
Russell L. Steere ◽  
Michael Moseley
Keyword(s):  
Fracture Surfaces ◽  
Aluminum Specimen ◽  
Specimen Holder ◽  
Freeze Etching ◽  
The Right

A redesigned specimen holder and cap have made possible the freeze-etching of both fracture surfaces of a frozen fractured specimen. In principal, the procedure involves freezing a specimen between two specimen holders (as shown in A, Fig. 1, and the left side of Fig. 2). The aluminum specimen holders and brass cap are constructed so that the upper specimen holder can be forced loose, turned over, and pressed down firmly against the specimen stage to a position represented by B, Fig. 1, and the right side of Fig. 2.

Adrenocorticotropin Production by a Mammary Carcinoma

1977 ◽  
Vol 35 ◽  
pp. 462-463
Author(s):  
K.S. McCarty ◽  
N.R. Wallace ◽  
W. Litaker ◽  
S. Wells ◽  
G. Eisenbarth
Keyword(s):  
Adrenocorticotropic Hormone ◽  
Small Cell ◽  
Hormone Production ◽  
Carcinoma Of The Breast ◽  
Ectopic Acth ◽  
Ultrastructural Studies ◽  
Subcutaneous Metastases ◽  
Ectopic Acth Production ◽  
The Right ◽  
Pituitary Carcinomas

The production of adrenocorticotropic hormone by non-pituitary carcinomas has been documented in several tumors, most frequently small cell carcinoma of the lung, islet cell carcinomas of the pancreas, thymomas and carcinoids. Electron microscopy of these tumors reveals typical membrane-limited "neurosecretory" granules. Confirmation of the granules as adrenocorticotropin (ACTH) requires the use of OsO4 as a primary fixative to give the characteristic cored granule appearance in conjunction with immunohistochemical demonstration of the hormone peptide. Because of the rarity of ectopic ACTH production by mammary carcinomas and the absence of appropriate ultrastructural studies in the two examples of such ectopic hormone production in the literature of which we are aware (1,2), we present biochemical and ultrastructural data from a carcinoma of the breast with apparent ACTH production.The patient had her primary tumor in the right breast in 1969. The tumor recurred as visceral and subcutaneous metastases in 1976 and again in 1977.

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