Irrationals not being numbers, and 1 not being 0.999..., are everlasting topics in sci.math, popping up all the time. Very simple yet forgotten methods of early mathematics can dissolve the problem.7
Approximating the square root of 2 by a number column which I reconstructed in 1979
1 1 2
2 3 4
5 7 10
12 17 24
29 41 58
70 99 140
and so on
99/70 is already a fine value for the square root of 2. (Analogous number columns approximate the square roots of 3 and 5 and the cube root of 2.)
Now let us look at the square root of 4 by drawing up the analogous number column
1 1 4
2 5 8
7 13 28
20 41 80
61 121 244
182 365 728
and so on
The ratios, for example 41/20 or 121/61, get ever closer to 2. This means that 2 as the square root of 4 is equally mysterious as the square root of 2.
Or that the square root of 2 is no less mysterious than 2.
As for 1 = 0.999... let me begin with the Horus eye series of Ancient Egypt, 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 or simply '2 '4 '8 '16 '32 '64
1 = '1
1 = '2 '2
1 = '2 '4 '4
1 = '2 '4 '8 '8
1 = '2 '4 '8 '16 '16
1 = '2 '4 '8 '16 '32 '32
1 = '2 '4 '8 '16 '32 '64 '64
From this you get
'2 '4 '8 '16 '32 '64 ... = 1
(The Horus eye series had an astronomical function, since a month of 30
days multiplied by '2 '4 '8 '16 '32 '64 yields 29 '2 '32 days or 29 days
12 hours 45 minutes for one lunation of 29 days 12 hours 44 minutes 2.9 seconds, modern average from 1989 AD - mistake of the old value less than one minute per lunation, or half a day in a lifetime. One eye of the Horus falcon was the sun, standing for a month of 30 days, his other eye was
the moon, standing for one lunation or synodic month.)
Another infinite series
1 = '1
1 = '1x2 '2
1 = '1x2 '2x3 '3
1 = '1x2 '2x3 '3x4 '4
1 = '1x2 '2x3 '3x4 '4x5 '5
1 = '1x2 '2x3 '3x4 '4x5 '5x6 '6
1 = '1x2 '2x3 '3x4 '4x5 '5x6 '6x7 '7x8 '8x9 '9x10 '10x11 '11x12 ...
'1x2 '2x3 '5x6 '6x7 '9x10 '10x11 ... = pi/4
Now for 0.999... being 1
1 = 10/10
1 = 9/10 + 10/100
1 = 9/10 + 9/100 + 10/1000
1 = 9/10 + 9/100 + 9/1000 + 10/10000
and so on
1 = 0.999...
Mathematical education should begin with really simple methods, not on
the level of Euclid. Would prevent some people from wasting their life
on kooky notions.
On Friday, April 21, 2017 at 10:02:41 AM UTC+3, Franz Gnaedinger wrote:[...]
Irrationals not being numbers, and 1 not being 0.999..., are everlasting
topics in sci.math, popping up all the time. Very simple yet forgotten
methods of early mathematics can dissolve the problem.
Approximating the square root of 2 by a number column which I reconstructed >> in 1979
On 10/18/2023 6:19 PM, bassam karzeddin wrote:
On Friday, April 21, 2017 at 10:02:41 AM UTC+3, Franz Gnaedinger wrote:[...]
Irrationals not being numbers, and 1 not being 0.999..., are everlasting >> topics in sci.math, popping up all the time. Very simple yet forgotten
methods of early mathematics can dissolve the problem.
Approximating the square root of 2 by a number column which I reconstructed
in 1979
If you can draw a square you just constructed the sqrt of 2.
On Thursday, October 19, 2023 at 8:24:46 AM UTC+3, Chris M. Thomasson wrote:
On 10/18/2023 6:19 PM, bassam karzeddin wrote:
On Friday, April 21, 2017 at 10:02:41 AM UTC+3, Franz Gnaedinger wrote: >>>> Irrationals not being numbers, and 1 not being 0.999..., are everlasting >>>> topics in sci.math, popping up all the time. Very simple yet forgotten >>>> methods of early mathematics can dissolve the problem.[...]
Approximating the square root of 2 by a number column which I reconstructed
in 1979
If you can draw a square you just constructed the sqrt of 2.
Who said that a squre isn't an existing mathematical object to be easily constructed?
And nothing wiuld make a ratio of two sucessive integers as one, FOR SURE
HINT: (9/10, 99/100, 999/1000, ...ETC)
Forget about using the decimal notation onceonly in your life to see the truth so clearely befor your eyes
BKK
On 10/19/2023 3:28 AM, bassam karzeddin wrote:
On Thursday, October 19, 2023 at 8:24:46 AM UTC+3, Chris M. Thomasson wrote:
On 10/18/2023 6:19 PM, bassam karzeddin wrote:
On Friday, April 21, 2017 at 10:02:41 AM UTC+3, Franz Gnaedinger wrote:[...]
Irrationals not being numbers, and 1 not being 0.999..., are everlasting
topics in sci.math, popping up all the time. Very simple yet forgotten >>>> methods of early mathematics can dissolve the problem.
Approximating the square root of 2 by a number column which I reconstructed
in 1979
If you can draw a square you just constructed the sqrt of 2.
Who said that a squre isn't an existing mathematical object to be easily constructed?p0 = -1-1i
p1 = 1-1i
p2 = 1+1i
p3 = -1+1i
draw lines:
p0 to p1
p1 to p2
p2 to p3
p3 to p0
You got a square. This has the sqrt of 2 in it.
And nothing wiuld make a ratio of two sucessive integers as one, FOR SURE
HINT: (9/10, 99/100, 999/1000, ...ETC)
Forget about using the decimal notation onceonly in your life to see the truth so clearely befor your eyes
BKK
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