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What is cutting edge maths? - Mathematics Stack Exchange To come back to your question, the cutting edge is often in the refinement and well considered combination of equations, 'paragraphs' in this metaphor Where the metaphor differs is that the english language allows for endless break down of the rules, such that hundreds of paragraphs can be written quickly, whereas a single mathematical
arithmetic - Can a piece of A4 paper be folded so that its thick . . . Say that during the cutting process, the cellulose fibers unravel somewhat, leaving only two layers of fiber Since the fibers are 2-20 nm in diameter , let's say that the two-fiber-layer sheets are about 10nm thick $2^{42} \times 10nm = 43,980 m$, which, according to Wolfram Alpha, is about five times the height of Mount Everest
Online tool for making graphs (vertices and edges)? Changing style of nodes and edges (color, shape, thickness of edge, line style, node size) Bending edges; Shortcuts support; Displaying the last action with possibility to undo; Copying, cutting, pasting of nodes and edges; Support for mobile and touch devices; The application is still in a development state – any suggestions and feedback are
geometry - Different proofs of the Pythagorean theorem? - Mathematics . . . Some popular dissection proofs of the Pythagorean Theorem --such as Proof #36 on Cut-the-Knot-- demonstrate a specific, clear pattern for cutting up the figure's three squares, a pattern that applies to all right triangles I have yet to find a similarly straightforward cutting pattern that would apply to all triangles and show that my same
geometry - Compass-and-straightedge construction of the square root of . . . For example, suppose you want to find the square root of 5 Construct a right triangle with side lengths 1 and 2 This can be done with straight edge and compass Then the hypotenuse has length $\sqrt{5} $ (times the unit) The procedure can get more complicated
geometry - Why is the volume of a sphere $\frac{4}{3}\pi r^3 . . . As the plane cutting through the solids moves, these blue squares will form $4$ small pyramids in the corners of the cube with isosceles triangle sides and their apex at the edge of the cube Moving through the whole bicylinder generates a total of $8$ pyramids
How can I find the points at which two circles intersect? $\begingroup$ There is only one plane in $\mathbb{R^2}$, and this is $\mathbb{R^2}$ What you do is the change of the coordinate plane or coordinate system $(\vec{a},\vec{b})$ do not define a coordinate plane you additionally need an origin which should be $\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)$, I think
How to calculate the intersection of two planes? Now if we look at the existing planes from the perspective of that direction, our 2 planes look like 2 lines, because we're viewing them both edge-on So we want to calculate what those 2 lines are We can get the direction of each line as the cross product of our new plane's normal with the original normal: