0/0 Equals Two (Fallacy)

0/0 Equals Two (Fallacy)
                    
                0/0  =  (100-100) / (100-100)
                       =  (10-10)(10+10) / 10(10-10)
                       =  (10+10) / 10
                       =  20 / 10
                       =  2
                0/0  =  2

                  Thus 0/0 = 2 is proved by the help of Mathematical Fallacy .

Mystery Math On 0/0

Mystery Math On 0
                   
                   In Mathematics most of the operations have been made easy using few tricks or even by normal methods . But many of us gets a great confusion in getting value this expression :


                                                                    0/0  =  ?
                 
                   Each person gives each value for this expression but none can go with single value with confidence. 
                  
                   In some point of view , the value of this expression  is  1 , as they compare this expression with the expression , 
                                                                    x/x  =  1 ( A Number Divided By Itself Is ONE )
                   
                    In other views , the value will be taken as 0 on comparing this expression with  ,
                                                                      
                                                                     0/x  =  0 ( ZERO Divided By Any Number Is ZERO )


                    Few consider the value of this expression as INFINITY , due to the expression ,


                                                                     x/0  =  INFINITY
                                            ( Any Number Divided By ZERO Is INFINITY )  
          
                   Thus there are THREE values considered for this expression - 1 , 0 , INFINITY. So which one of these values is to be considered as the exact value for this . We cannot choose any value as we wish and also it is impossible to go on with one value . Upon all these conditions , 0/0 is considered as an UNDEFINED FUNCTION or UNDEFINED VALUE . 

Impossible Mind Reader - Card Trick

Impossible Mind Reader - Card Trick

     Remove 25 cards from the pack and allow the spectator to shuffle and cut the cards as much as they want then lay the 25 cards out in 5 rows of 5 cards face upwards from left to right in neat rows following a sort of grid pattern.

    

      Ask the spectator to think of any one of the cards in any row and to tell you which row their card is located in. When they tell you, note the card at the left hand end of the row. Take up the cards, beginning first at the last or right hand card of the bottom line, placing it on the face of the card immediately above it and then place these 2 cards on top of the card immediately above, and so on up to the top.

      Do this with each of the rows in turn and you should be left with 5 piles of cards on what was the top row.

       Collect up the cards, placing the 5th (right hand) pile on top of the 4th, then this stack on top of the 3rd, then on top of the 2nd, etc, until you're left with a single stack of cards.

       Then once again, keeping the cards face up, deal then into another 5 horizontal rows as before. Ask the spectator to tell you once again which row their card is located in. When they tell you, look along the top or the bottom row for the card which you noted earlier was first in the row they had indicated. Above it or below in the row to which they now point, is the card which they originally thought of.

Etruscan Numerals

Etruscan Numerals


The Etruscan numerals were used by the ancient Etruscans. The system was adapted from the Greek Attic numerals and formed the inspiration for the later Roman numerals.There is very little surviving evidence of these numerals. Examples are known of the symbols for larger numbers, but it is unknown which symbol represents which number. The general argueement among the Etruscologists is :

Etruscan	Decimal
θu	1
zal	2
ci	3
śa	4
maχ	5
huθ	6
semφ	7
*cezp	8
nurφ	9
śar	10
*θuśar	11
*zalśar	12
*ciśar	13
huθzar	14
*maχśar	15
*śaśar	16
ciem zaθrum	17
eslem zaθrum	18
θunem zaθrum	19
zaθrum	20
cealχ	30
*huθalχ	40
muvalχ	50
śealχ	60
semφalχ	70
cezpalχ	80
*nurφalχ	90

Difficult Squaring

Square 2 Digit Number: UP-DOWN Method

Square a 2 Digit Number, for this example 37:

• Look for the nearest 10 boundary
• In this case up 3 from 37 to 40.
• Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
• Now mentally multiply 34x40
• The way I do it is 34x10=340;
• Double it mentally to 680
• Double it again mentally to 1360
• This 1360 is the FIRST interim answer.
• 37 is "3" away from the 10 boundary 40.
• Square this "3" distance from 10 boundary.
• 3x3=9 which is the SECOND interim answer.
• Add the two interim answers to get the final answer.
• Answer: 1360 + 9 = 1369

With practice this can easily be done in your head.

Fun With Maths - Binary Card Trick

Binary Card Trick

You put a deck of cards in your pocket, and invite anyone in the audience to call out a number between 1 and 15. Then you reach into your pocket, you take out a set of cards whose sum is the number that was called! How can you perform this magic trick? The Math Behind the Fact: This mathematical magic trick can be found in the reference and is based on the properties of binary numbers. Every number between 1 and 15 has a unique representation as a sum of some collection of the numbers 1, 2, 4, and 8. (To see which collection, just take the given number and successively subtract the largest number of 1, 2, 4, and 8 that is less than the given number. That number is part of your collection. The subtraction yields a new number; now repeat the process with this number, over and over, until you get 0.) The collection of numbers you obtain reveals the binary decomposition of the given number into sums of powers of two (in contrast to the usual representation of a number into sums of powers of ten). Now before the trick starts, pick an Ace, 2, 4, and 8 and put them on top of the deck, and then put the deck in your pocket. Then when a number between 1 and 15 is called out, take the binary decomposition of the number, and use that to determine which of the first four cards you will pull out. No one needs to know that you never need to use the other cards!

Fun With Maths - Perfect Shuffles

Perfect Shuffles

Figure 1 We know from the Fun Fact Seven Shuffles that 7 random riffle shuffles are enough to make almost every configuration equally likely in a deck of 52 cards. But what happens if you always use perfect shuffles, in which you cut the cards exactly in half and perfectly interlace the cards? Of course, this kind of shuffle has no randomness. What happens if you do perfect shuffles over and over again? There are 2 kinds of perfect shuffles: The out-shuffle is one in which the top card stays on top. The in-shuffle is one in which the top card moves to the second position of the deck. Figure 1 shows an out-shuffle. Surprise: 8 perfect out-shuffles will restore the deck to its original order! And, in fact, there is a nice magic trick that uses out and in shuffles to move the top card to any position you desire! Say you want the top card (position 0) to go to position N. Write N in base 2, and read the 0's and 1's from left to right. Perform an out-shuffle for a 0 and and in-shuffle for a 1. Voila! You will now have the top card at position N. (See the reference.) Example. Since 6 is 110 in binary notation, then the sequence IN-IN-OUT will move the top card (position 0) to position 6 (the seventh card). Presentation Suggestions: Have students go home and determine how many in-shuffles it takes to restore the deck to its original order. (Answer: 52.) You can also have students investigate decks of smaller sizes. As a project, you might even tell them part of the binary card trick and see if they can figure out the rest: whether 0 or 1 stands for an in/out shuffle, and whether to read the digits from left to right or vice versa. The Math Behind the Fact: This fact may come as somewhat of a surprise, because there are 52! possible deck configurations, and since there is no randomness, after 52! out-shuffles, we must hit some configuration at least twice (and then cycle from there). But 8 is so much smaller than (52!). See Making History By Card Shuffling. Group theory concerns itself with understanding sets and properties preserved by operations on those sets. For instance, the set of all configurations of a deck of 52 cards forms a group, and a shuffle is an operation on that group.