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Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.
Boggle gives you 3 minutes to find as many words (3 letters or more) as you can in a grid of 16 letters. You can also try the grid of 16 letters. Letters must be adjacent and longer words score better. See if you can get into the grid Hall of Fame !
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Tips: browse the semantic fields (see From ideas to words) in two languages to learn more.
||This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2010)|
The term is associated with a common visualization of complex numbers with points in the plane endowed with Cartesian coordinates, with the Y-axis pointing upwards: the "upper half-plane" corresponds to the half-plane above the X-axis.
It is the domain of many functions of interest in complex analysis, especially modular forms. The lower half-plane, defined by y < 0, is equally good, but less used by convention. The open unit disk D (the set of all complex numbers of absolute value less than one) is equivalent by a conformal mapping (see "Poincaré metric"), meaning that it is usually possible to pass between H and D.
It also plays an important role in hyperbolic geometry, where the Poincaré half-plane model provides a way of examining hyperbolic motions. The Poincaré metric provides a hyperbolic metric on the space.
One natural generalization in differential geometry is hyperbolic n-space Hn, the maximally symmetric, simply connected, n-dimensional Riemannian manifold with constant sectional curvature −1. In this terminology, the upper half-plane is H2 since it has real dimension 2.
In number theory, the theory of Hilbert modular forms is concerned with the study of certain functions on the direct product Hn of n copies of the upper half-plane. Yet another space interesting to number theorists is the Siegel upper half-space Hn, which is the domain of Siegel modular forms.