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I'm reviewing a wagering-proposition where I suspect the house has made a mistake in the odds it is offering. In a twenty-horse race (assuming all of the horses are of equal ability) the result of the first three finishers all being odd- or even-numbered was offered at three-to-one odds. This seems to defy logic, as two of the horses will have to be either even or odd. The proposition seems to boil down to: "Will the third horse (of the remaining eighteen) be the same type of number as the other two?". The true odds of this happening seem to only be slightly less than even, certainly nowhere near three-to-one. I want to rush to put the maximum-bet of $300 ($100, my mistake) down on this proposition, but being far from the smartest fellow on the planet, I figured I should double-check this with our learned and perspicacious mathematicians first. Thanks in advance!
Joefromrandb (
talk)
04:39, 10 April 2014 (UTC)
I'm making a flag, and I want to make sure I have the proportions right. Let's imagine that this flag is 1000 units wide and 500 units tall. Each arm of the cross has a thickness (A) of 100 units, and is centered on a line running, at a 26.57° angle, from one corner of the flag to the other. What is B, the length of white along the bottom edge on the left? -- Lazar Taxon ( talk) 11:40, 10 April 2014 (UTC)
Is it possible to color the vertices of a 24-cell red yellow and blue such that a rotation (or combination of rotations) would take the red vertices to where the yellow were and similarly the yellow to blue and the blue to red? Secondly, is there a coloring of the octahedral cells orange, green and purple so that the *same* rotations in the first question "rotates the colors" of the cells as well? Naraht ( talk) 15:48, 10 April 2014 (UTC)
Does the D4-symmetric tricolouring work for the cells, constructing the 24-cell as ?
Double sharp (
talk)
14:27, 13 April 2014 (UTC)
We know that addition and multiplication are commutative, but exponentiation is not. However, I also know this inconsistency:
Let's look at 2 number lines; the additive number line and the multiplicative number line. The additive line converts to the multiplicative line by replacing all with .
Every addition problem using numbers on the additive number line has a corresponding multiplication problem . That is, each number on the additive line becomes a number on the multiplicative number line. For example, becomes .
Every multiplication problem using numbers on the additive number line has a corresponding exponentiation problem . That is, and are replaced with and , but is retained, not replaced by . For example, becomes , not .
Suppose we had used a commutative version of exponentiation. This form of exponentiation can be notated . It can be defined as follows: for any and , . For example, becomes .
Do you notice that this "commutative exponentiation" shares several properties with addition and multiplication?? These are the commutative property, the associative property, the identity property (2 is the exponentiative identity for commutative exponentiation,) the special-value property (for addition; this number is ; for multiplication it is ; for commutative exponentiation it is ); and the inverse property (the exponentiative inverse of is the number for which .
Any thoughts on whether this can go in any Wikipedia article?? Georgia guy ( talk) 17:43, 10 April 2014 (UTC)
Mathematics desk | ||
---|---|---|
< April 9 | << Mar | April | May >> | April 11 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I'm reviewing a wagering-proposition where I suspect the house has made a mistake in the odds it is offering. In a twenty-horse race (assuming all of the horses are of equal ability) the result of the first three finishers all being odd- or even-numbered was offered at three-to-one odds. This seems to defy logic, as two of the horses will have to be either even or odd. The proposition seems to boil down to: "Will the third horse (of the remaining eighteen) be the same type of number as the other two?". The true odds of this happening seem to only be slightly less than even, certainly nowhere near three-to-one. I want to rush to put the maximum-bet of $300 ($100, my mistake) down on this proposition, but being far from the smartest fellow on the planet, I figured I should double-check this with our learned and perspicacious mathematicians first. Thanks in advance!
Joefromrandb (
talk)
04:39, 10 April 2014 (UTC)
I'm making a flag, and I want to make sure I have the proportions right. Let's imagine that this flag is 1000 units wide and 500 units tall. Each arm of the cross has a thickness (A) of 100 units, and is centered on a line running, at a 26.57° angle, from one corner of the flag to the other. What is B, the length of white along the bottom edge on the left? -- Lazar Taxon ( talk) 11:40, 10 April 2014 (UTC)
Is it possible to color the vertices of a 24-cell red yellow and blue such that a rotation (or combination of rotations) would take the red vertices to where the yellow were and similarly the yellow to blue and the blue to red? Secondly, is there a coloring of the octahedral cells orange, green and purple so that the *same* rotations in the first question "rotates the colors" of the cells as well? Naraht ( talk) 15:48, 10 April 2014 (UTC)
Does the D4-symmetric tricolouring work for the cells, constructing the 24-cell as ?
Double sharp (
talk)
14:27, 13 April 2014 (UTC)
We know that addition and multiplication are commutative, but exponentiation is not. However, I also know this inconsistency:
Let's look at 2 number lines; the additive number line and the multiplicative number line. The additive line converts to the multiplicative line by replacing all with .
Every addition problem using numbers on the additive number line has a corresponding multiplication problem . That is, each number on the additive line becomes a number on the multiplicative number line. For example, becomes .
Every multiplication problem using numbers on the additive number line has a corresponding exponentiation problem . That is, and are replaced with and , but is retained, not replaced by . For example, becomes , not .
Suppose we had used a commutative version of exponentiation. This form of exponentiation can be notated . It can be defined as follows: for any and , . For example, becomes .
Do you notice that this "commutative exponentiation" shares several properties with addition and multiplication?? These are the commutative property, the associative property, the identity property (2 is the exponentiative identity for commutative exponentiation,) the special-value property (for addition; this number is ; for multiplication it is ; for commutative exponentiation it is ); and the inverse property (the exponentiative inverse of is the number for which .
Any thoughts on whether this can go in any Wikipedia article?? Georgia guy ( talk) 17:43, 10 April 2014 (UTC)