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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
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
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Probability of forming triangle from breaking a stick Following your definition of X,Y, the joint choice of X,Y are uniform in the unit cell (density 1) The task remained is to find the cutting position of X and Y such that resulting 3 segments can form a triangle Consider case when Y > X (so three segments length are X, Y-X, 1-Y) Inserting the fact that sum of any two sides is greater than the
How to find the line that splits the area into two equal parts? Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
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
What is the proper geometrical name for a a rectangle with a semi . . . Here's a simulated clothoid track drawn in Mathematica: Just to show that the bends are honest-to-goodness clothoids, I drew the clothoid corresponding to the lower right portion of the track in full (the dashed gray one)