Inequality Notation: What Does it Mean?

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Inequality notation can include dots to represent multiplication, which is equivalent to writing (a)(c) > (b)(c). The Pythagorean theorem does not hold in elliptical geometry, as it is tied to the parallel postulate. However, there are generalizations of the theorem applicable in non-Euclidean geometries. For further details, additional resources like Wikipedia can provide more information. Understanding these concepts is crucial for grasping advanced mathematical principles.
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I was reading on inequalities and encountered a notation i haven't come across before.
an image of it is added to this post as an attachment.
 

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If you mean the dots, it is simply a different way of expressing multiplication.

so that is the same as

(a)(c) > (b)(c)
 
one other question i have.
Does Pythagorean theorem still work if you use elliptical geometry?
 
No, the Pythagorean theorem is in fact equivalent to the parallel postulate. So it doesn't work in elliptical geometry.

There are however generalizations of Pythagoras which do hold in non-Euclidean geometry. More information can be found on wiki: http://en.wikipedia.org/wiki/Pythagorean_theorem
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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