ΣΗμειώσεις Βαγγέλη Ψύχα
Κατηγορία: Ιδιωτικό
Μόνο όσα θέλω να είναι πλήρως ιδιωτικά
2023!!!
Χάρτες και προβολές
Κύκλος και ευθεία
https://www.geogebra.org/calculator/azecuwwj
Σφαίρα σε επίπεδο
https://www.geogebra.org/3d/rzfcyhwc
Πώς ξεδιπλώνω τη σφαίρα στο επίπεδο;
Είναι μεγαλύτερη η Ρωσία ή η Νότια Αμερική;
Ξεδιπλώστε το μανταρίνι στο επίπεδο:
Dimensions
Πώς και πόσα μαθαίνεις…
Λόγοι χωρίς έννοια…ή Πώς να μιλάτε χωρίς να λέτε τίποτα!
Προσοχή μαθηματικών
Math teacher Thomas Garrity knows how to get the full attention of the students
— Tansu YEĞEN (@TansuYegen) November 29, 2022
pic.twitter.com/aoaPRRX4fj
Φεγγάρι
Distance to the moon ?
— Fermat's Library (@fermatslibrary) November 30, 2022
In 129 BC Hipparchus used the following method to determine the distance to the Moon. pic.twitter.com/M7dTmXiz8A
Παίζοντας Dodgem
Παίζοντας dodgem εδώ.
https://www.geogebra.org/classic/hrc7hddk
Δύο παίκτες σε έναν πίνακα 4Χ4 έχουν τρία καπάκια τοποθετημένα σε δύο διαδοχικές πλευρές του τετραγώνου με κενή τη γωνία που συνορεύουν, όπως στο σχήμα:
Μετακινούν στη σειρά του ο καθένας ένα καπάκι μπροστά ή δεξιά ή αριστερά (όχι πίσω) με στόχο να εξάγουν όλα τα καπάκια από την απέναντι πλευρά από την οποία εκίνησαν.
Dodgem is a simple abstract strategy game invented by Colin Vout in 1972 while he was a mathematics student at the University of Cambridge as described in the book Winning Ways. It is played on an n×n board with n-1 cars for each player—two cars each on a 3×3 board is enough for an interesting game, but larger sizes are also possible.
Play
The board is initially set up with n-1 blue cars along the left edge and n-1 red cars along the bottom edge, the bottom left square remaining empty. Turns alternate: player 1 (“Left”)’s turn is to move any one of the blue cars one space forwards (right) or sideways (up or down). Player 2 (“Right”)’s turn is to move any one of the red cars one space forwards (up) or sideways (left or right).
Cars may not move onto occupied spaces. They may leave the board, but only by a forward move. A car which leaves the board is out of the game. There are no captures. A player must always leave their opponent a legal move or else forfeit the game.
The winner is the player who first gets all their pieces off the board, or has all their cars blocked in by their opponent.
The game can also be played in Misere, where you force your opponent to move their pieces off the board.[1]
Theory
The 3×3 game can be completely analyzed (strongly solved) and is a win for the first player—a table showing who wins from every possible position is given in Winning Ways, and given this information it is easy to read off a winning strategy.
David des Jardins showed in 1996 that the 4×4 and 5×5 games never end with perfect play—both players get stuck shuffling their cars from side to side to prevent the other from winning. He conjectures that this is true for all larger boards.
For a 3×3 board, there are 56 reachable positions. Out of the 56 reachable positions, 8 of them are winning, 4 of them are losing, and 44 are draws. [2]
