What is a counterexample for the conjecture? A number that is divisible by 2 is also divisible by 4. How many integers between 1 and 1000 are divisible by 5? What is the smallest number that must be added to 2,010 to obtain a number that is completeletly divisible by 19?
Example 3 One application of Napier’s rule (6) is to determine the sunrise equation for when the sun rises and sets at a given location on the Earth, and a given time of year. For sake of argument let us work in summer, in which the declination of the Sun is positive (due to ...
What is a statistical interaction? How do you determine whether a data point is an outside value? What is PESTEL analysis? How do you make a conjecture about the pattern 1,2,2,4,8,32? What is coordinate notation? What is the difference between quantitative and qualitative approaches?
A polyhedron is a three dimensional shape bounded by a series of flat planes which are known as faces. A simple example is a cube, a six-faced polyhedron made with square faces. There is actually some dispute in the math world about what constitutes a polyhedron, exactly, and some mathemat...
Rachel Greenfeld and I have just uploaded to the arXiv our paper “A counterexample to the periodic tiling conjecture“. This is the full version of the result I announced on this blog a few months ago, in which we disprove the periodic tiling conjecture of Grünbaum-Shephard and Lagarias-...
Those who believe in the ability of pyramids to concentrate or focus cosmic energy state that the shape is what is important, not the materials. A properly constructed pyramid, using the same geometry employed in the Egyptian pyramids, can be made of anything and still be effective. Some propo...
“The idea behind “Subgraph GNNs” is to represent graphs as collections of their substructures, a theme which can be found in the famous works by Kelly and Ulam in the 1960s on the Graph Reconstruction Conjecture [17]. Nowadays, the same idea is used to construct expressive GNNs which, ...
What is space-time made of? What is the fabric of space-time? John WheelerIt would be better to ask, what is the universe made of? And everything else will come in addition.So, for example, if gravity is a manifestation of the curvature of space-time, and space-time itself is emerg...
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Naively, it would then seem that there is not enough space inside such a point to support a rich enough structure of paths to recover the Galois theory of this field. In modern algebraic geometry, one addresses this issue by considering not just the set-theoretic elements of , but more ...