Legend about Sine and Cosine (continuation)

Beginning of Legend about Sine and Cosine

An anxious new that Sine and Cosine go to Mathematics, flew around the whole worlds quickly. Gods were in confusion. To this case they worked out all nascent problems. But now a problem arose up in the world of Numbers, and Numbers are not subject to Gods. Only Mathematics can establish order among Numbers.

Nobody of Gods never saw Mathematics all at once. Nobody knew exactly, that in their ideas about Mathematics is reality, and that by the figment of the imagination. All Gods sooner or later tried to know at Numbers, how correctly they understand one or another moment in the mathematical reasoning. In reply to all questions of Number enigmatically smiled and always pronounced a the same phrase: time will "Come, you will answer the question". Really, time passed and all became into the places. Some deductions were confirmed by life, some was dispersed, as fog. During all life of Gods their idea about Mathematics changed constantly.

And Gods got an exceptional case face to face to see Mathematics. She does not can to say no in attention to the faithful servants - to Sine and Cosine. Gods have a right to be present as the interested observers. From the decision of Mathematics will depend, in what world to live Gods farther.

When Sine and Cosine appeared before Mathematics, all looks of Gods were tied down only to Her. But Gods were waited by great disappointment - each of them saw that character which was by it created only. To not the least new detail.

What was seen to Mathematician by Sine and Cosine? Will pass many to time, before someone from Gods, possibly, will answer this question.

"That did bring you over to me?" - Mathematics asked at Sine and Cosine.

"We want, that you said, who of us main," - they pronounced.

"There are not main in family of Numbers. All Numbers are equal," - Mathematics repeated all the known truth.

"It is but as Unit?!" - Sine and Cosine exclaimed amicably.

"It is Unit such is exact Number, as all other numbers. Yes, at Unit the special status. But this status needs to be deserved. You know perfectly, to what Numbers and what this status is appropriated for," - Mathematics answered imperturbably.

"Then say to us, who is main from us two? We all the time argue and can not decide in any way," - stubbornly repeated over and over again Sine and Cosine.

"Reasonable creatures always can agree inter se. Unfortunately, you such are not," - Mathematics pronounced with bitter taste.

All Gods stopped beating in a fright. To declare reasonable creature unreasonable is means to deprive his rights on life. Did mathematics take away capital punishment to two representatives of immortal family of Numbers?! Such decision was not laid in consciousness of Gods. To give Numbers in power of Death is equipotent to capital punishment to the whole surrounding world!

"Do you want to be equal to unit? Do you want, that one of you always was more main than other? Do you want, that I stopped your dispute?" - Mathematics continued after short meditation. Anger was heard in voice of Mathematics, - "You are two capricious babies, which did not manage to become adults. Your place is in a corner," - Mathematics was slightly softened, Gods breathed with relief, - "Here my decision:"

sin2α + cos2α = 1

Gods stopped beating in bewilderment. They looked around on parties, trying to understand, what Mathematics did. Seemed, the world had remained former, but almost elusive differences were felt in everything. Gradually to Gods sense of this event began to come. Mathematics sentenced Sine and Cosine to perpendicular symmetry! Such usual to all World of Symmetry disappeared forever. The new world - World of Perpendicular Symmetry appeared.

Сontinuation will be

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