Maths

[Luke-Chesters]

@The_Letter_Wriggler

For Q1, would it not have to be -1?

-1 + 1/2 gives -1/2

-1 x 1/2 gives -1/2

[The_Letter_Wriggler]

@Luke-Chesters #91748
Are you asking? So it seems you are not positive with your answer! Ha, ha.

[The_Letter_Wriggler]

Just thinking – How do we know if a line is straight? What is it judged by?

[bridges]

@The_Letter_Wriggler
Q4 the unique solution for
1 2 ?
? 4 ?
? ? ?
has a 9 in the top right corner, not a 3.
Q7 a+b=a+d so b=d
a+c=a+d so c=d=b
a+d=b+d so a=b=c=d
Q8
28 8 20 2
3 21.5 32.5 1
22 18.5 -14.5 32
5 10 20 23

[Rhydwen23]

#91790 @The_Letter_Wriggler

A straight line is defined by its length. A straight line is the shortest distance between two points. Builders, decorators and gardeners, amongst others, will use a “line” (a piece of string drawn taught) to mark out a straight line.

[The_Letter_Wriggler]

@Rhydwen23
I don’t see how a STRAIT line can be defined by its length!
‘The shortest distance between two points’ that well known statement, for me, leaves out the word unobstructed.
Also what if I place two dots on a piece of paper and use a ‘strait-edge’ to draw a line to connect the dots, then I lay the paper around a cylinder so the dots
become closer together is it still a strait line? A curved strait line maybe? But no longer the shortest distance between the two dots!
Deformation, yes but the line itself is unaltered. Hope you get my drift.

My post was:
How do we know if a line is straight? What is it judged by?
Can we prove a line is strait? If we use an instrument we need the prove that that is strait also. Haven’t gone into any research, math or otherwise
it was just idle thougth.

[The question of what it means to be straight can only be answered relative to the space you are considering! In your example you wrap the space around a cylinder, changing the space, but then consider the surface of the cylinder as a subspace of the 3-dimensional space it lies in. The original line was straight in the classical sense, which can be phrased as “any two points on the line are as far apart in the line as they are in the plane. That is no longer true on the cylinder since once you wrap far enough round you can find points on the wrapped line which are closer on the cylinder than they are in the line itself. That is you can get from one point to the other faster using a short cut on the surface of the cylinder. It is even more obvious that you can take shortcuts once you are allowed to cut across the cylinder in the 3 dimensional space. However, what is true on the cylinder is that short enough segments of the wrapped line are still distance minimising, so the wrapped line is “locally” a geodesic” from the point of view of the cylindrical surface. That is definitely not true one you consider the corkscrew line in three dimensional space. Harry]

[The_Letter_Wriggler]

Thanks for you reply Harry.
Yes I was going from PLANE GEOMETRY to SOLID GEOMETRY not to mention DESCRIPTIVE GEOMETRY
and surfaces like a curved triangular surface calls for GEODESIC GEOMETRY possibly leading us to ANALYTIC GEOMETRY OF SPACE
Other geometries are PROGECTIVE, DIFFERENTIAL and INTEGRAL.

[Or metric, or even coarse geometry, with the latter detecting only the geometry of a space “at infinity”. An amazing invention of some friends and colleagues around the world. Harry]

[Rhydwen23]

Terminology

I was thinking about some characteristics of the activity we’re undertaking, which may be considered good or even essential in some circumstances, and ask if the characteristics have a name. They all concern the process of getting from clear text to cipher text and back again and with a consideration of transmission or storage. Any cipher text is for illustration and doesn’t represent an actual encryption.

1. The set of characters in the cipher text is guaranteed to belong to the same set of characters used in the plain text. So, for example, if the plain text is composed of upper case Latin characters, then so is the cipher text. Does that property of the encipherment process have a name? I guess there are distinctions between exactly the same set and taken from the same set.

THEQUICKBROWNFOXJUMPSOVERTHELAZYDOG
to
FGHAABNNMCYRTSKLMWOSPPKFPLASBTYQWHD
and not
Ka*!wtsAGH97£$NnaGHKC?98FAgh8776?CV

2. The size of the cipher text is guaranteed to be no greater than the size of the plain text. So, for example, if the plain text is composed of ten characters, then the cipher text is guaranteed to be no longer. Does that property of the process have a name? Important for storage and transmission. Anything offering compression will be a special case.

HELLOWORLD
to
9%NcFG*vJ$
and not
1642A992N4565B2388H

3. The process of decipherment will recover from interruption and loss, or corruption of part of the cipher text during transmission or storage. Obviously the damaged part will be lost, but if the decipherment proceeds correctly after the damaged section. Does that characteristic have a name?

[madness]

3. For stream ciphers, you want “self-synchronizing”.

4. You didn’t ask, but there are such things as error-correcting codes. Check out Shannon codes as an example.

[Rhydwen23]

In reply to my own question #92467, what is the term for?..

1. The set of characters in the cipher text is guaranteed to belong to the same set of characters used in the plain text.

It looks as though a ‘finite set’ for the character set and a ‘finite group’ for the characters and the operation is a reasonable place to start. It certainly looks an interesting area to investigate. I hope this comment doesn’t offend and mathematicians who understand the subject. If it isn’t correct, I’d appreciate a pointer in the right direction.

[Author]

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