base one l. van warren. start at the beginning… what is a placeholder?
TRANSCRIPT
Start at the beginning…Start at the beginning…
What is a placeholder?What is a placeholder?
• 100 + • 10 + • 1 • 100 + • 10 + • 1 11 22 88
• 102 + • 101 + • 100 • 102 + • 101 + • 10011 22 88
• 100 + • 10 + • 1 • 100 + • 10 + • 1 11 22 88
+ • 10 + • 1+ • 10 + • 1100100 22 88
+ + • 1+ + • 1100100 2020 88
+ ++ +100100 2020 88
100100 2020 88
11 22 88
+ = ?
+ = ?
+ = ?
Meaning we canrepresent any sum
in the same counting system.(given sufficient time)
Meaning we canrepresent any sum
in the same counting system.(given sufficient time)
- = ?
- = ?
- = ?
- = ?
- = ?
- = ?
- = ?
- = ?
- = ?
- = ?
- = ?
The antistickrequires another bit
that makes base two!
The antistickrequires another bit
that makes base two!
The antistick isa negative stick with
the annihilation property:
The antistick isa negative stick with
the annihilation property:
The second numbertells us the
number of copiesof the first.
The second numbertells us the
number of copiesof the first.
And visa versaAnd visa versa
This demonstrates thatmultiplication in base one
is commutative.
This demonstrates thatmultiplication in base one
is commutative.
Base One SquaresBase One Squares
Squaring isa special case
of multiplication.
Squaring isa special case
of multiplication.
Choosing a different symbol reminds us of the
meaning of “squaring”.
Choosing a different symbol reminds us of the
meaning of “squaring”.
Or:Or:
How do we findthe square rootin base one?
How do we findthe square rootin base one?
“Find the number thatwhen multiplied by itself
gives the original number.”
“Find the number thatwhen multiplied by itself
gives the original number.”
If the number isa perfect square,the square root is
the length of one side.
If the number isa perfect square,the square root is
the length of one side.
Division, like subtractionis not closedin base one.
Division, like subtractionis not closedin base one.
Base One TrigonometryBase One Trigonometry
We must introducesome new symbols.We must introducesome new symbols.
These symbols arecontainers forcopies of our
counting symbol.
These symbols arecontainers forcopies of our
counting symbol.
Name relationships.Name relationships.
Base One ProbabilityBase One Probability
Ask some friendsto show you a number
by holding up their hands.
Ask some friendsto show you a number
by holding up their hands.
Questions?Questions?