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Answer : Here's one part of it. As far as polygons go, a triangle is the only one that is defined by its side lengths. If you have a triangle of sides 5,6, and 7, there is only one shape it can take. The same cannot be said of other polygons. Imagine a square. It can be squished into a diamond with the same side lengths. There is SSS congruence for triangles, but no analogous congruence for other polygons. That's what diagonal bracing does in physical structures. Creates triangles. As you asked about the strength of a triangular shape then let me introduce to the triangular chain consisting of three rigid links or bars connected to each other by pin joints(allowing rotation between two joined links) . The degree of freedom (n) of a plane chain is given by the Grasshoff's law as n = 3 ( l − 1 ) − 2 j − h n=3(l-1)-2j-h n = 3 ( l − 1 ) − 2 j − h for a triangular chain we have l = no. of links = 3 l=\text{no. of links}=3 l = no. of links = 3 j = no....

Answer : Let G G G be reflection of A A A about E F EF EF . Clearly E G = A E = E D EG=AE=ED EG = A E = E D and ∠ G E D = ∠ A E D − ∠ A E F − ∠ F E G = 10 8 ∘ − 2 4 ∘ − 2 4 ∘ = 6 0 ∘ \angle GED = \angle AED - \angle AEF - \angle FEG = 108^\circ - 24^\circ -24^\circ=60^\circ ∠ GE D = ∠ A E D − ∠ A EF − ∠ FEG = 10 8 ∘ − 2 4 ∘ − 2 4 ∘ = 6 0 ∘ . Hence G E D GED GE D is an equilateral triangle. So G D = D E = D C GD=DE=DC G D = D E = D C and ∠ G D C = 4 8 ∘ \angle GDC=48^\circ ∠ G D C = 4 8 ∘ . Hence ∠ D C G = ∠ C G D = 6 6 ∘ \angle DCG=\angle CGD=66^\circ ∠ D CG = ∠ CG D = 6 6 ∘ , ∠ D G E = 6 0 ∘ \angle DGE=60^\circ ∠ D GE = 6 0 ∘ , and ∠ E G F = ∠ F A E = 5 4 ∘ \angle EGF =\angle FAE = 54^\circ ∠ EGF = ∠ F A E = 5 4 ∘ . So angles C G D , D G E , E G F CGD, DGE, EGF CG D , D GE , EGF sum up to 18 0 ∘ 180^\circ 18 0 ∘ . So G G G lies on F C FC FC . So ∠ D C F = 6 6 ∘ \angle DCF = 66^\circ ∠ D CF = 6 6 ∘ and by symmetry ∠ F D C = 6 6 ∘ \angle FDC=66^\circ ∠ F D C = 6 6 ∘ . It foll...

Answer : For div tag there is already default property display:block given by browser. For anchor tag there is not display property given by browser. You need to add display property to it. That's why use display:block or display:inline- block . It will work. .btn { display:block; height: 300px; width: 300px; border-radius: 50%; border: 1px solid red; } <a class="btn" href="#"><i class="ion-ios-arrow-down"></i></a> .round-button { width:25%; } .round-button-circle { width: 100%; height:0; padding-bottom: 100%; border-radius: 50%; border:10px solid #cfdcec; overflow:hidden; background: #4679BD; box-shadow: 0 0 3px gray; } .round-button-circle:hover { background:#30588e; } .round-button a { display:block; float:left; width:100%; padding-top:50%; padding-bottom:50%; line-height:1em; margin-top:-0.5em; text-align:center; color:#e2eaf3; font-fami...

Answer : Any rigid framework, hence all regular polygons, can be converted to a triangle-free equivalent. Simply chaining copies of the 12 12 12 -vertex triangle-free braced square shown in the question (which I discovered) along the two collinear edges gives a rigid line segment of arbitrary whole number length without triangles: Then any triangular grid can be mimicked without triangles as follows (all straight fuchsia edges are made with the graph chaining construction above, all black edges are single sticks): For example, to brace the hexagon without triangles: However, the above hexagon bracing is quite big. Another approach to triangle-free bracing is the virtual edge : in any embedding of the cubical graph with one edge removed, the distance between the two degree- 2 2 2 vertices (incident to the missing edge) must always be 1 1 1 . This leads to the following triangle-free rigid regular hexagon in 16 16 16 vertices and 29 29 29 edges (Shibuya commit proof): Th...

Answer : You probably were setting the width of your canvas using CSS. Altering the width of a canvas element in CSS stretches the pixels within the canvas Eg. <canvas style='width:400px;height:400px'></canvas> Instead, you need to use the width and height properties of the canvas element itself to define how many pixels the canvas contains. Correct way: <canvas width='400px' height='400px'><canvas>