Mathematics 3º ESO
Thursday 14 June 2018
YOKAKUS
Yohaku:
A New Type of Number Puzzle
A yohaku is a new type of number puzzle that will test your number
sense and problem solving skills. Each yohaku is either an additive or a
multiplicative puzzle (as indicated by the symbol in the bottom right of the
grid). Your task is to fill in the empty cells such that they give the sum or
product shown in each row and column.
ADDITIVE
PUZZLES
Sunday 10 June 2018
Las fincas del tío Mauricio
El tío Mauricio tiene varias fincas pero estas no le dan más que problemas. Ayuda al tío Mauricio a resolver estos problemas:
Las fincas del tío Mauricio
Las fincas del tío Mauricio
Thales and the Great Pyramid of Cheops
Thales of
Miletus ( c. 624 – c. 546 BC) was a Greek philosopher, mathematician and
astronomer from Miletus in Asia Minor (present-day Milet in Turkey). He was one
of the Seven Sages of Greece. He travelled widely in the Mediterranean region,
including to Egypt, which was long the dominant historical power in that area.
Egypt of course is home to the great pyramids at Giza, which were already ancient,
having been built more than two thousand years previously.
Thales asked the Egyptian about the height of the Great Pyramid of Cheops, but nobody knew the height of the Great Pyramid, so he set about measuring it himself. His method initiated a powerful approach in geometry - similar triangles.
Then, as the length of his own shadow was equal to his height, so the height of the pyramid was equal to the length of its shadow. That is to say, the pyramid's height was equal to the sum of half the side of its base and length of its exceeding shadow.
If height and length are equal, then they are directly proportional with constant of proportionality 1. Equivalently, he could calculate this directly:
d/c = b/a =1
So after he measured c, then he knew the height of the Pyramid (d)
His conclusion was that the height was about 481 feet, or 146.5 m.
Exercises
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