Headminister's Announcements
~Welcome to Staries Academy!
It's pretty simple here and I think you'll like this place! This is where all our students shine like stars! And we'll spread some light to you too!
You may wear whatever you want.

No GodModing~
No Advertising~
Be literate.
USE QUOTATION MARKS WHEN TALKING AND ITALICIZE THINKING!
Try to include EVERYONE.
No using *does something*
Or ~does something~
Or - does something -
Or anything like that!
Fighting is okay...but don't kill each other!
It's alright to swear...
Romance...uhh....I guess okay.
Keep it at a PG-13 level.
If you do not post anything within a week,
you'll get kicked out.
private message [PM] YOUR CHARACTER SKELETON TO ME!!!

If you need to edit your forms, please tell the secretary what you need updated and she'll fix it.
Have fun!



Classes & Schedule!

YOU MUST TAKE 4 MAIN CLASSES -one of each subject- AND PICK 2 ELECTIVES!
Clubs are OPTIONAL!!
The order of the classes will be PMed to you if you enroll!

-- Main Classes --
English Period 1
Math/Mathematics Period 2
Science Period 3

-- Electives --
Art
Music
Ceramics
Cooking
Computer Science
Graphics and Designing

-- Clubs --
Travel
Photography
Art Appreciation
Nature
Literature
Tennis
Soccer
Basketball
Baseball
Volleyball
Football
Cheerleading

Schedule -
9:00-9:50 AM -- English
10:00-10:50 AM -- Math
11:00-11:20 AM -- Break
11:30 AM - 12:20 PM -- Science
12:30-1:20 PM -- Lunch
1:30-2:20 PM -- Lunch Break
2:30-3:20 PM -- Elective 1
3:30-4:20 PM -- Elective 2
4:30-10:00 PM -- Free Time/Club Meetings
10:00-10:10 PM -- Get ready for bed
10:15 PM - BEDTIME!

*10-minute time gaps are for time getting to class~*

heres how classes work

the main classes are altogether everybody does it in the forum room

the electives are the things you do by yourself

like art i will give you an assignment like "draw a rose"
then you draw a rose then post it online

cooking is i tell you to cook something, take a picture of it and post it
or i tell you like go find a recipe for blah blah

Music is i tell you to like go find a hip song, or a modern song, or a song from 1990

computer science, graphics, ceramic i dont know if you find what i can do with those you get an extra 50 points!!!

grades:

A+ = 50 points
B = 40
C = 30
D = 20
F = 00

most points at the end of the week gets some gold :D

Be the first ten and also get 100 points!!!


if you are offline you get graded on you excuse. if you are you know what happens[you take the class and get a grade](classes are easy), if you are and im not just post *checks in for 9:30 class of... and you willl get 10 points for each class you checked in. Okay?


Staff: 50 points for each staff that helps me out like substitute and stuff


Weekends~
Free time the whole day! You can leave school grounds(with a slip obtained from the headmistress) but not the city!




Enroll now at Starlight Academy!

Please fill out this form and hand it to the secretary at the office.

Staries Applications

Student Application
NEW STUDENT~
Name:
Age:
Gender:
Personality:
Race:
Background:
Special Abilities: (limit is 5)
Talents/Hobbies:
Dorm: (the dormitory you want to be in)
Electives choosing:
Clubs: (optional)
Appearance: (link to picture please!!)
COLOR:


Staff Application
NEW STAFF~
Name:
Age:
Gender:
Personality:
Race:
Background:
Special Abilities: (limit is 5)
Talents/Hobbies:
Position: (teacher, secretary, librarian, coach, etc.)
Teaching: (for teachers)
Dorm:
Appearance: (link to picture please!!)
Color:


Students/Staff Accepted
students~
Holly
Megan
staff~
Nagihiko

Dorm 1
-Holly Drake
-Beki Crompton
-Chastity Melrose Chandler
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Dorm 2
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Dorm 3
-Megan Grimm
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Dorm 1
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Dorm 2
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Dorm 3
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Dorm 1
-Nagihiko Fujisaki
-Ryuu Tsuji
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Dorm 2
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Dorm 3
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School Campus

Features:
Administrative Building
Teachers' Lounge
50 Classrooms, some empty
Girl and Boy Dorms
Swimming Pool
Sports Area

Name: Chastity Melrose Chandler
Age: 17
Gender: Female
Personality: Usually a very bubbly, happy, and outgoing person, but gets angered and annoyed easily and can be very naive and clumsy and is slightly obsessed over designer labels
Race: Human
Background: Chastity was born into an unbelievably wealthy and powerful family, and always had a very lavish lifestlye but was always overshadowed by her much more glamorous and special ability-talented older siblings. Tired of the feeling of constant pressure and feeling as though everyone was watching her every move, Chastity decided to enroll in the school as a way to get away from her overbearing parents.
Special Abilities: Control over ice, but not very good at it
Talents/Hobbies: Likes to meet new people and travel, read, and have fun, and is good at volleyball
Dorm: 1
Electives choosing: Art and Music
Clubs: Volleyball
Appearance: http://media.photobucket.com/image/g...er/blonde5.jpg

Name: Megan Grimm
Age: 17
Gender: Female
Personality: Rude, mean, almost heartless, some times trys to be nice.
Race: A reaper
Background: Born in the under world she was raised to be heartless. She found it boring down there so she went to the surface and found a school that would take her in. She real does not care for others, but can be easily embarrassed
Special Abilities: Wind, fire, and shadows.
Talents/Hobbies:
Dorm: 3
Electives choosing:
Art
Cooking
Clubs: None
Appearance: Megan




Name: Nagihiko Fujisaki
Age: 18
Gender: Male
Personality: Nice, but strict on teaching
Race: Confidential
Background: Confidential
Special Abilities: teaching and the ability to hide his true appearance
Talents/Hobbies: reading
Position: Principal, Teacher, Head Minister
Teaching: Everything except electives
Appearance: Confidential

Name: Ryuu Tsuuji
Age: 19
Gender: Male
Personality: Fun and sometimes strict
Race: Half Demon
Background: Confidential
Special Abilities: Sword master, Claws of Death, Flying
Talents/Hobbies: Sports, Games =D
Position: Vice principal/head minister and teacher
Teaching: Electives
Appearance: http://media.photobucket.com/image/r.../Ryuu.jpg?o=37

Student Competition

Chantity:100 points
Beki:100 points
Megan:110 points

Staff Contest

Ryuu:200 points

Mr. Fujisaki walked into the room and looked around.."I think my Students are Late"

Holly walked into the classroom and sat down, setting her books down in front of her on the desk.
"Good morning, Mr. Fujisaki." she nodded, giving a small smile as she clasped her hands together, waiting for the other students.

Mr. Fujisaki said "hmm seems your the only one in class...That's good lets start with math"

Lets start with Chapter one :Use of the Slide Rule as a Teaching Tool part 1

# Introduction

In the days before calculators and personal computers an engineer always had a slide rule nearby. These days it is difficult to locate a slide rule outside of a museum. I don't know how many of those who have used a slide rule ever thought of it as an analog computer, but that is really what it is. As such, I think that it is an ideal tool for teaching the mathematical concept of transformations. With the proper scales, a slide rule can be used not only to multiply but to find the third side of a right triangle and add velocities relativistically. In order to introduce the concepts that will be used, we will start with the simplest type of slide rule - one that is made up of two ordinary rulers.

# Using Rulers for Addition

Two rulers can be lined up as in the figure below to show that 5 + 3 = 8. Note that in order to do this it is not necessary to know how to add or even to be able to count. All that is required is to line up the start of the top ruler with the symbol "5" on the bottom ruler; locate the symbol "3" on the top ruler and the symbol "8" below it on the bottom ruler.

# For the purposes here I am going to define a slide rule as using two copies of the same scale, with one scale moving relative to the other. Actual slide rules may use two different scales, which could either be stationary or mobile with respect to the other.

# Analog Computers

An analog computer performs a calculation by transforming numbers into physical quantities, combining these physical quantities and then converting the result into the result of the calculation. The way in which a slide rule is an analog computer should be clear - a numerical computation (in this case addition) is performed by changing numbers into a physical representation (distances); the distances are added and the resultant distance is reverse transformed into the result of the numerical calculation.

# Mirror Worlds


I think this is kinda boring but who cares :D

Holly nodded as she took down the notes on her notepad, using her favorite black ink pen.
"This is really boring... But whatever..."

"good you are doing great ready for chapter two?"

Holly just gave a small yawn and nodded, propping her head up with one of her hands. She looked almost half asleep.

i wouldnt be surprised if i fell asleep either .-.

# Figure 2 above shows diagrammatically what is happening. Imagine two worlds, a number world X below the black horizontal line and a distance world above it. In the number world 3 is added to 5 to get 8. The arrows above "5" and "3" represent the transform of these numbers into distances. The symbol "//" represents the operation of adding the two distances to produce the distance to the right of the "//". The arrow above the "8" represents the transform of that distance into the number 8. There are thus two ways to get to the "8". Symbolically, 5 + 3 = D-1(D(5) // D(3)). That is, adding 5 and 3 is the same as adding their distances and then taking the inverse transform to convert the distance 8 into the number 8.

# Translations

The addition slide rule was compared above to a mirror. Perhaps a more apt metaphor would be a translation.

Suppose you traveled back in time to the days of the Roman Empire. You notice someone doing arithmetic using Roman numerals and you want to verify your understanding of this numeric representation. Let T be the transformation from Arabic numerals to Roman numerals. According to what you were taught T(5) = V, T(III) = 3 and T(8) = VIII.

You observe that this particular person seems to be using ".." to stand for "+". You hand over a sheet of paper with V .. III written on it. When the person writes VIII on the paper this increases your confidence that the above transformation is correct. You have established a degree of internal consistency. We can think of addition as taking two input values to produce an output value. Since the output is determined by the inputs, for one process to be a translation of the other it is sufficient for equivalent inputs to result in equivalent outputs. (5+3) is the output of the Arabic numeral arithmetic. T(5)..T(3) is the output of the Roman numeral arithmetic. For the outputs to be equivalent we must have T(5)..T(3) = T(5+3) . If we could prove that in general T(X)..T(Y) = T(X+Y)then we could say that the one process is a translation of the other.

For the addition slide rule we have D(X) // D(Y) = D(X+Y) . The combining of distances is a translation of the addition of numbers. It does not matter that numbers and distances are different entities. Adding numbers is structually equivalent to combining distances. The next section states this in more formal terms.



# Isomorphisms

Any invertible relationship of the form
T(x & y) = T(x) % T(y)
is called an isomorphism (Greek for "same form").
The & and % stand for operators on the elements of the appropriate domain. In the above example & = + and % = //.

The inverse transform T-1 provides a way of reversing the roles of the mirror domain and the original domain or, alternatively, of reversing the direction of the translation.

Let u=T(x), v = T(y).

Then x = T-1(u), y = T-1(v).
Substituting in the above equation,
T(T-1(u) & T-1(v)) = u % v.

Applying T-1 to both sides,
T-1(u % v) = T-1(u) & T-1(v).

In an isomorphism variables in one domain are related to each other through & operator in exactly the same way as the transformed variables relate to each other through the % operator.

In particular, one operator will be commutative if and only if the other is:

x & y = y & x if and only if
T(x) % T(y) = T(y) % T(x).


This is easy to show:
If y & x = x & y then
T(y) % T(x) = T(y & x) = T(x & y) = T(x) % T(y).



All operations for which there are slide rule scales are commutative since adding distances is commutative.

# A Little Philosophy

Equations used to express scientific laws are an expression of an isomorphism between nature and mathematics. Analog computers are a reversal of the usual computation. Ordinarily, the isomorphism is used to determine a physical quantity by measuring the other physical quantities in the equation and then using the equation to solve for the missing quantity. In an analog computer, a number is computed by converting the other numbers in the equation into physical quantities and then using the physical situation to determine the missing value.

We use isomorphisms in our daily lives all the time. When we look in a mirror or read a map we are using isomorphisms. Whenever we solve a problem by an analogy to another problem there is an implied isomorphism.

In mathematics, isomorphisms are used to express relationships between abstract mathematical objects. The slide rule can be used by the teacher to both teach the concept of isomorphism and to unify, and thus simplify, several different concepts by showing how they are examples of isomorphisms.

I am going to present logarithms as an isomorphism between multiplication and addition, without reference to exponents. If you think that this presentation is unnatural, consider that this is the point of view taken by the discoverer of logarithms, John Napier, in the seventeenth century. He was unaware of the connection between logarithms and exponents until it was brought to his attention. Napier was just looking for a simpler way of multiplying.

# Logarithms, Multiplication and Composition

The logarithmic function satisfies the relationship
log (x * y) = log(x) + log(y).

The log function is an isomorphism. It transforms a
multiplication problem into an addition problem. Since
addition of numbers is isomorphic to addition of
distances, consider the effect of applying the distance
function D to both sides of the equation.

D(log(x*y)) = D( log(x) + log(y) ) = D( log(x)) // D(log(y) )
D(log(x*y)) = D(log(x)) // D(log(y))

It follows that the transform (D log) formed by composing
the D and log transforms is an isomorphism. The same
process could be used to show that in general the
composition of two isomorphic transforms is an isomorphic transform -
the mirroring of the mirroring of a domain is itself a
mirroring of the domain;
the translation of a translation is a translation of the original.

The construction of a slide rule for multiplication
follows from the above equation. If the distance
that a number is placed is equal to the log of the
number then the result is the standard slide rule.
Figure 3 shows how the slide rule is used to
multiply 10 and 1000.




Shortly after their discovery it was realized that logarithm functions loga(x) were the inverse of exponential functions ax. For convenience, let us write the exponential function as EXP(X) and the logaritm function as LOG(X) for some common base a.

Since LOG(X) is an isomorphism and EXP(X) is its inverse, then by what was shown above we get:

EXP(X+Y) = EXP(X) * EXP(Y),
which is an expression of the law of exponents.

# Right Triangles and Parallel Resistances

What made it possible to construct a slide rule for multiplication was that the log function provides an isomorphism between multiplication and addition. There are other isomorphisms to addition. Consider right triangles. The length of the hypotenuse is given by:

c2 = a2 + b2 .

If we let s(x) = x2 and define a & b as the length of the hypotenuse of a triangle with sides of lengths a and b then s(a & b) = s(a) + s(b) and we have our isomorphism. If a slide rule is constructed so that the distance along the slide rule is equal to the square of the number then the slide rule can be used to find the third side of a right triangle given the other two.

Figure 4 shows such a slide rule set up for the familiar right triangle with sides of 3, 4 and 5.



As another example consider the equivalent electrical resistance for two resistors in parallel given by 1/r = 1/r1 + 1/r2. This can be computed using a slide rule with distances equal to the reciprocal of the number.

A virtual right triangle slide rule Java program (Takes a minute or two to download)

# Relativistic Addition of Velocities

The final slide rule will compute relativistic velocity.
As a quick explanation of what this is, consider a
person walking forward with velocity u in a train
traveling with velocity v. Then the exact velocity w of
the person relative to the ground can be expressed
using the isomorphic relationship

(c + w)/(c - w) = (c + u)/(c - u) * (c + v)/(c - v), where c is
the speed of light (about 186,000 miles per second).

To avoid having to use the speed of light in our calculations
we can express all the velocities as fractions of the
speed of light. Dividing the numerator and denominator
of all three terms by c gives

(1 + p)/(1 - p) = (1 + q)/(1 - q) * (1 + r)/(1 - r), where
p = w/c, q=u/c and r = v/c.

Applying in succession the log and distance
functions to both sides gives:

D(log ((1 + p)/(1 - p) )) =
D(log( (1 + q)/(1 - q) )) // D(log( (1 + r)/(1 - r))).

To construct a slide rule to add velocities, set the
distance of a fraction x equal to
log( (1+x) / (1-x) ).

Figure 5 shows a slide rule for adding velocities.

A virtual velocity addition slide rule

# Proof by Isomorphism

Consider again the original formula for velocity
(c + w) / (c - w) = (c + u)/(c - u) * (c + v)/(c -v).

Let u & v be the sum of velocities u and v.
Let T(x) = (c + x)/(c - x).
Then T(u & v) = T(u)*T(v)

How do we add three velocities? In the example
of the person walking with velocity u in a
train traveling with velocity v, let s be the velocity
of the earth relative to the sun. What is the
velocity of the person relative to the sun?

Velocities can only be added two at a time. There
are two ways of doing this and we would hope that
they come out the same.

We could first find the velocity of the person
relative to the earth and then add this velocity to
the velocity of the earth relative to the sun.
This would give

T(s & (v & u)) = T(s) * T(v & u) = T(s) * (T(v) * T(u))

On the other hand we could first find the velocity of
the train relative to the sun and then add the
person's velocity. We then have

T((s & v) & u) = T(s & v) * T(u) = (T(s) * T(v)) * T(u).

The two values are of course the same. The reason
for this is that multiplication is associative, i. e.,
(a * b) * c = a * (b * c). We see that this causes
addition of velocities to be associative -
s & (u &v) = (s & u) &v.

The above argument could have been used for
any isomorphism. Thus we have the property
that isomorphisms preserve the associative
property just we showed earlier that they preserve
the commutative property. We could have used
this property to state immediately that it does
not matter which of the two ways the velocities
are added because multiplication is associative.

It could also have been argued that using the
velocity slide rule, it is obvious that it does not
make any difference in which order the velocities
are added. This is because the addition of distances
is both commutative and associative and any
calculation for which we can construct a slide
rule must therefore also be both commutative and
associative.

In the above formula for velocity addition it is
possible to solve for w to get

u & v = (u + v)/ (1 + u*v/c2).
To show that addition of velocities is associative
we could have then solved explicitly for both
(s & (v & u)) and ((s & v) & u), but this involves
a great deal more effort.



We can also apply the above results to the parallel resistor and
right triangle examples.

Using the notation in the section on right triangles, the
distance (x & y) that results from East and North displacements
of x and y is given by s(x & y) = s(x) + s(y). To generalize to
three dimensions we get s(s & y & z) = s(x) + s(y) + s(z).

For combining several parallel
resistors we get:

1/r = 1/r1 + 1/r2 + ... + 1/rn.

Mr. Fujisaki Yawned

(( You should probably quote that, since you're earning a bunch of gold for it... Unless you're writing it yourself. o___o ))

Holly just skimmed through and wrote all the important stuff, too bored to write it all. When she was done, she turned to a new page and started randomly doodling, her mind off in her own little world.

Mr. Fujisaki said in a Yawning voice " Just three more short chapters" IF neither of us sleep than" He Yawned "You get an A+"

Dazzle Your Friends

Consider the formula x & y defined as x & y = xy + x + y. This does not initially seem very impressive. To see that there is more than meets the eye, let's compare (2 & 3) & 5 and 2 & (3 & 5).

In the first case, (2 & 3) & 5 = (2× 3 +2 + 3) & 5 = 11 & 5 = (5 × 11 + 5 + 11) = 71. In the second case, 2 & (3 & 5) = 2 & (3 × 5 + 3 + 5) = 2 & 23 = (2 × 23 + 2 + 23) = 71. So it appears that x & (y &z) = (x & y) & z.

That this is true in all cases can easily be seen by using the transform T(x) = x +1. We have (xy + x +y) + 1 = (x + 1) × (y + 1). T(x & y) = T(x) × T(y). Our operation & is isomorphic to multiplication. We could therefore create a slide rule for our operation as we did for relativistic velocity addition by applying in turn the log and distance addition isomorphisms, but to impress friends and family all you have to do is make use of the associative property.

Write a sequence of numbers on a piece of paper, for example 1, 2, 3, 7 and 11. Give the person a calculator and tell the person to choose any two numbers and replace them with the product of the two numbers added to the sum of the two numbers, that is replace x and y with xy + x + y. This new number can be placed anywhere in the list. Tell the person to conitnue doing this until only one number remains. You then tell what number this is. In this case the number will be (1 + 1)(2 + 1)(3 + 1)(7 + 1)(11 + 1) -1 = 2303.

Holly nodded as she looked back up and went back to writing notes. She broke for a short moment to look around, but nobody was there yet, still. Weird.
She went back to writing notes.

From Isomorphism to Duality

We can go further. The fact that NOT is the transform function for both AND and OR means that we can apply both transforms simultaneously. For example, consider the following distributive identity between AND and OR which is analogous to the distributive operation of multiplication and addition:

X AND (Y OR Z) = (X AND Y) OR (X AND Z).

We can prove this statement by substituting all 8 combinations of X, Y and Z. We should also test the reasonableness of the statement by using an example.
"I will speak to Sarah and (I will speak to) John or Raymond." is the same as "I will speak to Sarah and John or I will speak to Sarah and Raymond."

Apply NOT to both sides of the equation. Using the AND isomorphism gives the following on the left side.

NOT(X AND (Y OR Z)) = NOT X OR NOT (Y OR Z)

Applying the OR isomorphism gives

NOT X OR NOT (Y OR Z) = NOT X OR ((NOT Y) AND (NOT Z))

Each of the arguments has been negated and the ANDs and ORs have been interchanged. The same happens on the right side of the equation. We get

NOT X OR ((NOT Y) AND (NOT Z)) =
((NOT X) OR (NOT Y)) AND ((NOT X) OR NOT Z)

We can get rid of the NOTs by setting X'=NOT X, Y'=NOT Y, Z'=NOT Z, so that what end up is the same form as we started except the ANDs and ORs have been interchanged:

X' OR (Y' AND Z') = (X' OR Y') AND (X' OR Z')

For every identity a new one can be created by interchanging AND and OR.

The relationship between AND and OR is referred to as a duality. In this case we have a duality between operators. There are different types of duality but the general principle is that a dualism exists when true statements can be generated from other true statements by interchanging two terms.
Addendum - Slide Rule Scales for Raising a Number to a Power

Since, in general, xy is not equal to yx, there can not be slide rule scales for raising a number to a power if we require both scales to be the same. However, if we remove the requirement for isomorphism we can use two different scales to achieve our purpose. We can create the slide rule scales if we can find two different functions T and U that satisfy:

T(xy) = T(x) + U(y)

We then create the slide rule having T(x) as the bottom scale and U(y) as the top scale. Standard slide rules do this by having T(x) = log(log(x)) and U(y) = log(y).

To see why this works, find log(log(xy)):

log(log(xy)) = log(y*log(x)) = log(y) + log(log(x)).

"Last Chapter......" YESSSSS!!!!!!!!!

Holly gave a small clap and wrote down the notes as fast as she could, even though she was still almost half asleep.

" A+ and an extra ten points for being here in ten minutes is science but who cares im tired so science is ofF!!!! have fun with your free time you have until 2:30 to have fun all you want then its ELECTIVES

Chastity ran into in the school building, and stopped to take a breath. She groaned, knowing that she must've been really late. It wasn't her fault that she was too used to having a maid wake she up instead of an annoying alarm clock, right?

She stopped for a minute to admire her new Chanel satin sandals heels, and accidentally ran and bumped into another girl. "Oh, sorry!" she said.

"Oh wow. Okay." Holly smiled as she flipped her notebook closed and walked out into the hall.

Suddenly, another girl bumped into her and apologized.
"Oh, no, it's okay." Holly nodded.

A girl dashed down the hallway, skidding to a stop just before she hit the other two girls. She gave a big grin "Hi! I'm Beki" she held out her hand and tilted her head slightly, making her pink pigtails bob slightly.

"Oh, uh." Holly looked the other girl up and down. "Well, hi there." she smiled softly, shaking her hand.
"I'm Holly. Holly Drake. What about you, what's your name?" quickly, she looked at her watch.
"Ah... I'm tired... I should go take a nap. Well, I guess I'll see you all later. Bye!" she said as she waved and ran off to the dorms, to take a nap.

Nagihiko walked out of the teacher's lounge and saw the girls talking. He walked over and said "hi! ^^ My name is Nagihiko Age 18"

Chastity smiled and said, "I'm Chastity. Chastity Chandler."

Beki looked at the other girl, smiling. She loved meeting new people. She made a little wave, dropping the books that were under her arm in the process. She quickly ducked down to pick them up. She giggled "I can be so clumsy sometimes" her voice was clearly british, with a weak, Yorkshire accent.

Chastity smiled at Beki, and said, "Same here," then asked Nagihiko, a bit surprised, "Aren't you a bit, well, young to be a teacher?"

Beki raised an eyebrow at Chastity. Wow she thought I'd never be brave enough to talk like that to a teacher