kjodle/Flatland
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

Added math formatting to chapter 15 to match original

Browse Source
This commit is contained in:
Kenneth John Odle 2023-06-23 13:09:32 -04:00
parent cb86c326c7
commit d217cb6e3b
1 changed files with 11 additions and 11 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

22
main.tex
View File

@ -2147,27 +2147,27 @@ make one large Square, with a side of three inches, and I had hence proved to
my little Grandson that --- though it was impossible for us to see the inside of my little Grandson that --- though it was impossible for us to see the inside of
the Square --- yet we might ascertain the number of square inches in a Square by the Square --- yet we might ascertain the number of square inches in a Square by
simply squaring the number of inches in the side: ``and thus,'' said I, ``we know simply squaring the number of inches in the side: ``and thus,'' said I, ``we know
that three-to-the-second, or nine, represents the number of square inches in a that $ 3^2 $, or 9, represents the number of square inches in a
Square whose side is three inches long.'' Square whose side is 3 inches long.''
The little Hexagon meditated on this a while and then said to me; ``But you The little Hexagon meditated on this a while and then said to me; ``But you
have been teaching me to raise numbers to the third power: I suppose have been teaching me to raise numbers to the third power: I suppose
three-to-the-third must mean something in Geometry; what does it mean?'' $ 3^3 $ must mean something in Geometry; what does it mean?''
``Nothing at all,'' replied I, ``not at least in Geometry; for Geometry has only ``Nothing at all,'' replied I, ``not at least in Geometry; for Geometry has only
Two Dimensions.'' And then I began to shew the boy how a Point by moving Two Dimensions.'' And then I began to shew the boy how a Point by moving
through a length of three inches makes a Line of three inches, which may be through a length of three inches makes a Line of three inches, which may be
represented by three; and how a Line of three inches, moving parallel to represented by 3; and how a Line of three inches, moving parallel to
itself through a length of three inches, makes a Square of three inches every itself through a length of three inches, makes a Square of three inches every
way, which may be represented by three-to-the-second. way, which may be represented by $ 3^2 $.
Upon this, my Grandson, again returning to his former suggestion, took me up Upon this, my Grandson, again returning to his former suggestion, took me up
rather suddenly and exclaimed, ``Well, then, if a Point by moving three inches, rather suddenly and exclaimed, ``Well, then, if a Point by moving three inches,
makes a Line of three inches represented by three; and if a straight Line of makes a Line of three inches represented by 3; and if a straight Line of
three inches, moving parallel to itself, makes a Square of three inches every three inches, moving parallel to itself, makes a Square of three inches every
way, represented by three-to-the-second; it must be that a Square of three way, represented by $ 3^2 $; it must be that a Square of three
inches every way, moving somehow parallel to itself (but I don't see how) must inches every way, moving somehow parallel to itself (but I don't see how) must
make Something else (but I don't see what) of three inches every way --- and make Something else (but I don't see what) of three inches every way --- and
this must be represented by three-to-the-third.'' this must be represented by $ 3^3 $.''
``Go to bed,'' said I, a little ruffled by this interruption: ``if you would talk ``Go to bed,'' said I, a little ruffled by this interruption: ``if you would talk
less nonsense, you would remember more sense.'' less nonsense, you would remember more sense.''
@ -2184,12 +2184,12 @@ Straightway I became conscious of a Presence in the room, and a chilling
breath thrilled through my very being. ``He is no such thing,'' cried my Wife, breath thrilled through my very being. ``He is no such thing,'' cried my Wife,
``and you are breaking the Commandments in thus dishonouring your own ``and you are breaking the Commandments in thus dishonouring your own
Grandson.'' But I took no notice of her. Looking around in every direction I Grandson.'' But I took no notice of her. Looking around in every direction I
could see nothing; yet still I felt a Presence, and shivered as the cold could see nothing; yet still I \textit{felt} a Presence, and shivered as the cold
whisper came again. I started up. ``What is the matter?'' said my Wife, ``there whisper came again. I started up. ``What is the matter?'' said my Wife, ``there
is no draught; what are you looking for? There is nothing.'' There was nothing; is no draught; what are you looking for? There is nothing.'' There was nothing;
and I resumed my seat, again exclaiming, ``The boy is a fool, I say; and I resumed my seat, again exclaiming, ``The boy is a fool, I say;
three-to-the-third can have no meaning in Geometry.'' At once there came a $ 3^3 $ can have no meaning in Geometry.'' At once there came a
distinctly audible reply, ``The boy is not a fool; and three-to-the-third has distinctly audible reply, ``The boy is not a fool; and $ 3^3 $ has
an obvious Geometrical meaning.'' an obvious Geometrical meaning.''
My Wife as well as myself heard the words, although she did not understand My Wife as well as myself heard the words, although she did not understand