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Ulysses 31

Do you know something from Greek mythology? Odysseus wandering through the Mediterranean on his return from the Trojan War until it can return to Ithaca with his wife Penelope and son Telemachus. The mighty Zeus on Mount Olympus, Polyphemus the Cyclops, and Hades, hell, the realm of the dead.

And do you remember this? I loved it.

feel I just wanted a little girl.

Stahni Zdarma Milena Velba

comes Christmas time peace, love and reconciliation. Open our hearts to the spirit of Bethlehem. May the example of the family of Nazareth comforting our homes and open a glimmer of hope.



A light coming from the east, opening the door to Christmas, time to be born of hope, solidarity and love.




May this Christmas I want to convert each flower, each pain star, every smile and every tear in a sweet heart abode for Jesus, our Savior.



is the desire of the management team and teachers of the School Fray Luis Beltrán

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Spanish and American Dates [The Problem of the Week] The age of the grandfather

several weeks ago proposed this little problem to the apprentices:

Mauritius, the grandfather of Joseph, is certainly not the centenary, but very old. We can say that last year, his age was a multiple of 8, and that next year is divisible by 7. How old is Mauritius?

The solution can be found under the interesting picture that we propose.

[Matenavegando mathematicians looking for long-lived, we have found the life of Leopold Vietoris an interesting article published Gaussianos.com . Vietoris was a mathematician Austrian born in 1891, which made important contributions in the field of topology. It is possible, according to this article, which is the mathematical Vietoris oldest known, for he died in 2002 at 110 years old. It is also the oldest Austrian, and her second marriage is the seventh longest marriage by adding the age of both spouses, as his second wife died in 101. The list is long-lived marriages in this wikipedia article.]

Solution:

The problem is to find a multiple of 8 and a multiple of 7 to differentiate by 2 units. Once found, the age of Mauritius will be the middle number.

multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120 ...

The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119 ...

As Mauritius is not centenary, multiples greater than 100 we can rule out.

If you look carefully, there are two candidate pairs: 40 and 42 on one side, 96 and 98 on the other. But in the first case of Mauritius would be the age of 41 years, and this is no old age. The second case is more logical age Mauritius must be 97 years . Thus the previous year of age was 96 years (multiple of 8) and next year will be his age 98 years (multiple of 7).

Enlargement:

Such exercises can be solved by mathematical tools called congruences . In mathematical language, if we call x the age of Mauritius, then:

x ≡ 1 (mod 8)

x ≡ -1 (mod 7) ≡

The symbol is like sign of the same but with three horizontal lines instead of two, and in this context means is consistent with . For the properties of congruences, the second equation can be replaced by x ≡ 6 (mod 7)

As the greatest common divisor of 7 and 8 is equal to 1, the Chinese remainder theorem assures us that this system in congruences has a solution. To find the solution can be carried out as follows:

The two previous equations would be the same as saying:

x = 1 + 8k

x = 6 + 7j, where k and j represent any integer.

Multiplying the first equation by 7 and the second for 8 are:

7x = 7 + 56k

8x = 48 + 56j

Subtracting the second equation minus the first and we have:

x = 41 + 56 (j - k)

As k and j are arbitrary integers, the difference between them is also an arbitrary integer, then x is equal to 41 plus a multiple of 56 arbitrary:

x = 41 + 56mm, or what is the same:

x ≡ 41 (mod 56)

We have therefore to x can take the values \u200b\u200b41, 97, 153, 209, 265, ... And could even take negative values, such as -15, -71, -127, -183, -239, ...

Of all the possible solutions for x, we choose the most logical, 97, and therein lies our answer.

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STAGE ONE COMPLETED

Then came New Year ...



The tempera been completed, a few leaves have fallen, the crayons are cortitos ...
But how many things we have today in the courtroom the first day were not: your drawings in a corner, a broken toy (probably unintentionally), the folder that you've started Traveling with your family remember? Loupes with which investigated and the clothes they play ... the brush, the palette ...
Many memories will remain in our hearts ... certainly feel that it was a moment in our lives but we were special to share and give us as we are.
made us feel we chose the best profession in the world.


THANKS!
☼ Red Room
Board ☼
Celeste ☼ Yellow Room
☼ Blue Room

Love is playing paths toward us, and give thanks to life for having traveled.

Today I can only tell you that it will be hard to say goodbye and that this bit of your childhood, for always going to unite. ADRIANA
WITHIN WITHIN
SILVANA
WITHIN WITHIN
IVANA MARIA DE LOS ANGELES