If mathematics was invented to cope with sensory information linking it to reality. I would just like to say that all sensory information is real. Just because you could be dreaming doesn't mean you are.

]]>So what possible transformations are isometries of the plane? You might think that there were a whole bunch of them: rotations, reflections, and translations. (A reflection followed by a translation is sometimes called a glide reflection.) In fact the picture is simpler than that: it turns out that reflections and translations can be built up from rotations alone! A translation in a certain direction is simply a reflection in two axes perpendicular that direction, while a rotation about a point O is a reflection in two axes through O.

Hence any translation is a reflection in two axes perpendicular to the direction of translation whose distance apart is half the distance to be translated.Hence any rotation is a reflection in two axes through the centre of rotation whose angular separation is half the angle to be rotated through.

]]>It is always possible to slice a three-layered ham sandwich with a single cut of a knife in such a way that each layer of the sandwich is divided into two exactly equal halves by the cut.

The ham-sandwich theorem can be proved using the Borsukâ€“Ulam theorem.

]]>I learn that it is possible to make a tetradecahedron with just regular hexagons and squares.

It is also possible to make a truncated icosahedron with regular pentagons and hexagons.

Let , and suppose that is a continuously differentiable function on . Then:One of the many applications of this theorem is using it to show that:

by writing

where denotes the greatest integer part of x, and is the Euler-Mascheroni constant.]]>or, more precisely:

where M is the so-called Meissel-Merten's constant, with value approximately equal to 0.2614972128476427837554268386086958590516...

This result is known as Merten's second theorem.

]]>It has been a while now, how did everything go? Looked at Numberphile page, it looks pretty good.

]]>]]>

]]>

After Minkowski translated my theory in the form of mathematics I could no longer understand my own theory.

The relationship between math and physics is tenuous at best. Feynman was actually a pretty good EM guy and one of its principles was actually first expounded by him. You should read DZ's comments about the turn mathematics took with the arrival of Cauchy, the turn it took in the 20th century.

]]>