Kay raised her hand. "Seven is considered to be a spiritual number because it is illusive and contains veils which must first be uncovered, one after another, before illumination will ultimately be found. Seven is also the most powerfully magical number. This is why," Kay hesitated for a moment, "Lord Voldemort created seven horcruxes."

Heshasa who had been taking notes feverishly, looked up at the mention of Voldemort's name. Putting down her quill to listen if more on this subject would arise.

Professor Fox nodded as the students gave their answers. "Ah, yes, those are all interesting observations." He looked over the students. "Well, you are right, it is a very mystical and magical number. Because of the fact that it is popularly known as a mystical number, there are numerous misunderstandings concerning it."

He walke dto the front of the desk and leaned against it, looking at the students. "Whomever said it is the number of days in a week, this is due to the fact that the Week was originally defined by the astronomical bodies known to the ancient Greeks and Romans, which were 7 in number."

He gave a slightly strange look at Nadia's answer. "Ah... Well, that is an... Interesting observation Ms. Rey. You are right concerning the number 360. However, if we were to divide a circle into radians, then the number of radians in a circle is 2 times pi. Then, no number divides it equally. Interesting point nonetheless." He paused, then continued, "Concerning the pyramids, the outer angle of pyramids is defined simply by physical limits on the pyramids themselves. In this case the similarity of the numbers is coincidence. Finally, I would disagree with you about your observation of 22 divided by 7. Its similarity to pi is superficial at best, and I would prove to you that you could find arbitrarily higher integer numbers that would yield better approximations of pi. That is neither here nor there however, good input nonetheless."

"Ms. Harrison, you and Ms. Rey are both absolutely correct concerning the fact that seven is often attributed as 'the most powerful magical and mystical number'. Though that is not to say it is the most important. I believe I've already answered your question about the days of the week." Professor Fox seemed to almost twitch at the mentioning of Lord voldemort and Horcruxes. "Ahh, yes... Well, Tom Riddle certainly was an accomplished Arithmancy student from what I gather of history books. Unfortunately, he misunderstood the complexities of Arithmancy." He said somewhat hesitantly before continuing, "Now I will have no more mentions of that particular use of the number 7 in my classroom. Is everyone clear on this?" He added stressfully, looking at the rest of the class, "Is there anything more anyone would like to add before we continue?"

Linnea was busily copying down notes. Why she even thought she could handle this class was beyond her. She enjoyed maths, but this was giving her a headache, probably cos of the questions her grandfather would ask if she even thought of spouting off information given. "Why?" It ALWAYS came down to why. Drove her nuts. Why this, why that, she sometimes thought him nothing more than a toddler, but then would understand the reasoning behind it. Instead of just accepting what was "known" she should find out why it was accurate, why she should believe it, and why it matters.

She would ask her grandfather's why questions later, right now, she didn't want to get lost........

Astoria looked over at Kay with wide eyes then turned back to Professor Fox. He seemed like he was very angry at the mention of Lord Voldemore and the seven horcruxes. She knew the history of Lord Voldemort because her grandfather lived in the time of Voldemort, so she knew the stories. She sighed and nodded her head as Professor Fox said not to mention that use of the number seven. She couldn't think of anything else the number seven had to do with, so she sat and waited for another question.

Professor Fox sighed, the students seemed intent on not participating again. At any rate, he simply supposed he would lecture if that was what they wanted.

"Very well, let's move on to the properties of the number 7. Like 3, 7 is a lucky number, one of the primes in the 'lucky prime' group of numbers. For this reason it is often attributed to luck. Furthermore, 7 is a very mystical and magical number in its own right, which is the reason behind the vogue and sort of mystique it has developed as a number over the years. Also, 7, being the largest and last of the basic primes -that is, those prime numbers between 0, and 9- is also associated with longevity and permenance." Professor Fox wrote a few of the terms down on the board: Magic, Mysticism, Magical Stability, Magical Permanence.

"For this reason, you will find 7 is actually sort of a taboo number of sorts in transfiguration, where permanence and spell longevity is often avoided for all but very specific transfiguration spells. 7, due to these properties is also associated very strongly with the phoenix, which was brought up by Ms. Arbon earlier. Phoenixes posses both intense magical properties, as well as intense longevity, as well as dragons, for which the number is also associated. But that's enough concerning magical beasts, your care of magical creatures professor will know far more on the subejct than me."

"The initial magical properties of seven were first discovered in the 13th century. Since then, talented Arithmancers have occasionally found more magical properties of the number. The first interesting property of the number is the fact that 7 perfectly smooth cylinders or long rods are the only number of such objects that can be fastened togther without the shape changing. Hence its stability, balance, and permanence. We will be experimenting with this in a moment." He paused and watched the students, "Are there any questions concerning specifics of the magical properties of 7 before we begin?"

Kay looked over her notes several times and noticed that the professor was covering odd numbers instead of going in numerical order. She was a bit concerned because he brushed over the magical properties of seven. Kay raised her hand and began to speak, "Professor Fox, could you please provide more details on the magical properties of seven?"

A little bit at lost if the professor had actually understood the cirle division or hadn't, Nadia shhok her head and raised her hand again, "I have understood, while seven possesses qualities of dreaminess, spirituality and psychic awareness, negatively it can be dubious, deceptive and insincere. Is this a correct description?"

Hesitantly, she added, "And... not a question about the number seven especifically, but why are we studing the prime numbers first? I mean, I'm just curious."

Professor Fox sighed, and looked down at the floor while Kay asked her question, nodding along as she asked. "Yes Ms. Harrison, well, as I mentioned there are numerous magical properties associated with the number 7. To mention a few specific elements here... 7 is the maximum number of two dimensional translations possible of a given pattern. What that means in general is rather esoteric, what it means specifically for witches and wizards is that all two-dimensional spells, such as... Spells which create moving pictures, etc. have a maximum possible number of variations that though depending on the specific spell, is a number that is a multiple of 7: 7,14,21,28... What have you. 7 is a strongly independent number, as such though it has highly magical properties, often enhancing or strengthening or creating longevity for spells, often, the process of using seven components of spells or magic requires much more external work than say... Using 3 components. Because of the difficulty required to work 7 components into any given spell, 7 components or inclusions are often used when magically sealing objects, as it is more difficult for wizards attempting to break the seal to discover other means of breaking said seal." He looked back to the class, hoping he had not lost them. "Did any of that help you for now Ms. Harrison? If you have nay more specific questions, you can always ask me after class." He nodded, then took in a breath before continuing, "Are we ready to progress then?"

Sara jotted down the notes. People were asking questions all over the place.

Kay listened attentively to Professor Fox as she added the information to her growing parchment of notes. When she finished writing, she set her quill down and raised her hand. "Professor Fox, thank you for the detailed explanation. I have no further questions."

Astoria jotted down what professor Fox said as notes. He knew his stuff about Arithmancy in her opinion. She popped her fingers from writing so much and tied her hair up in a ponytail with a pink ribbon. She looked back up at Professor Fox and raised her hand.

"No questions from me Professor. Please continue with the lesson."

Noel jotted down some numbers and notes, arithmancy was never her best subject, it all seemed so confusing to her. She tried to comprehend the numbers and there meanings as best she could, but she knew she'd forget them by the end of the day.

Professor Fox watched Nadia and sighed, she was obviously one of those students that always wanted more and more information. "Yes. Ms. Rey, what can I help you with? Ah. Well, you need not consider any of these numbers in terms of 'positive' and 'negative' qualities. They are simply numbers with attributes that affect magic. The positive and negative aspects are purely the creations of the dualistic human mind. Numbers, Ms. Rey, unlike people, are not deceptive. Concerning why we are studying primes, if you will recall, I explained at the beginning of class that all numbers can be represented as the sum of two primes. While non-wizard 'mathematicians' have yet to prove this, I assure you it is true. Hence, if all numbers can be represented as primes, does it not make sense to study primes first, as they are the building blocks of all numbers in our world?." He leaned against the wall, sighing slightly. "You seem confused still about the circle as well Ms. Rey. I assure you, while a noble and understandingly simple metaphor, I would make mention of the fact that the number 360 cannot be divided by 0. Hence, as I'm sure you will admit 0 is a true number as well, you will note that the metaphor is flawed. If you have any further questions, I encourage you to seek me in my office after class." He sighed and tried to look encouraging to the younger students. "I know this is all a lot to take in at once students, but does anyone have any other questions?"

"Ms. Fletcher, while I appreciate your willingness to participate. If you do not have a specific question, please do not raise your hand." He said as the strange student raised her hand without a question.

He sighed and leaned over, removing a large box from beneath the front desk. Professor Fox then removed a large number of what looked like small 8 inch thin wands. Setting them on his own personal chalkboard, they appeared to melt. Every student that had taken their own chalkboard then had 13 of the small sticks appear on their desks, along with a piece of string.

"Now, I have given everyone some sticks and some string, I would like you to try and tie various numbers of sticks together, and see which numbers of sticks remain in a fixed shape, without shifting. I think you'll find once you properly tie 7 sticks together, they will remain suitably stable, whereas no other combination will. If there are any questions please ask." He nodded encouragingly, "Feel free to talk peacefully with your friends and neighbors as you try this exercise. I will be walking around the room to check your progress."

Nadia mouthed an 'oh'. Now it was clear where exactly the thought was flawed. She hadn't considered, well, it was an understatement, about cero. Then again, it made one wonder if all numbers could be represented as the sum of two primes, because, how did it apply to the cero(0) and one(1) numbers? Arg, mathematics hadn't been her strenght at Muggle school...

OK, maybe she needed to review some of her notes before making any more questions and make a fool of herself.

Instead, Nadia turned her attention to the matter at hand, to the strings and sticks, first staring as if it was some sort of puzzle before she put herself to work it out. Now how would they tie the sticks together? One over the other? Because sure as heck it would shift. All together then? But then what did he mean by shifting. Sighing and still not sure if she had taken the intructions correctly, she grabbed a handful of the sticks and placed them 'standing' on the table with one hand, rounding them up with a string with the other. It was only 5 sticks now and it was... holding it pretty fine it seemed. Then she tried with 7 and it would still stand on its own. Now with a number over seven...

Rosa didn't quite understand most of this arithmancy, but it was interesting... she got her sticks and tied two of them together with real knots, on the scouting way. then she tied two other sticks together and put all of them up, tying a horizontal stick between the two, making it some sort of tentshape. it was still a bit wobbly, so she tied one stick between one left front paw and one right back paw and another one between the others. then she put it on the table again. it was really stable. she grabbed three of the other sticks and tied them together on the same way she'd done with the two sticks. then she stuck the sticks in different directions, and it was standing, stiff and not wobbly, except for when she pushed it in one direction. she looked at the remaining three sticks and wondered what to do with those.

Professor Fox had been wandering around the room. Noticing the students didn't seem to be getting the idea, he held up a set of four sticks. "Students. You are to tie the sticks in bundles. The sticks within the bundles will shift position, moving around within the string tie. Once you have tied 7 together, you will notice they will not shift." He said, showing an example to the students.

Rosa looked up and sighed unaudible when she heard she was to tie them in bundles. she'd just been hoping on an interesting class on constructions... she untied her sticks and made a bundle of two, of three, of four, of five, of six and of seven. and noticed that they really didn't shift any longer. she looked at her bondle and wondered why.

"oooh" said luna picking up her sticks and making 7 sets of sticks and tieing them together in a bundle like the proffessor's
"like this?" she said to proffessor fox

Astoria had never really experienced the horror of being publically embarassed in public until this class. For some reason, the teacher just didn't like her very much. She wouldn't normally care, but she really liked this class and she didn't want to drop the class because of the professor. She sighed and tied the sticks together. She was shocked to find that he was right! The sticks were no longer shifting.

"Awesome." she mumbled to herself.

Sunny manipulates the string and the sticks, slowly becoming frustrated. Finally she gives up on the lower numbers and starts with tying all seven sticks into a bundle. As Professor Fox had suggested, the sticks remained stationary, much to her relief.

Arkee glared at the clumsy bundle of sticks in her hand.

"Professor," she began warily, her hand slightly raised in the air, "I don't think that you're right about this... I've got seven and it's still falling apart."

She closely examined her bundle once more.

"One, two, three, four, five, six... six? Oh! No wonder," she exclaimed in relief, laughing a little. "I was always terrible in mathematics. It's a wonder that I'm taking this course!"

Suddenly, a look of bewilderment came over her face.

"Wait, why am I taking this course? Did I even sign up for it? Am I supposed to be in another class right now?!"

She frantically searched her bags for her timetable, which had conveniently been non-existant at the time, owing to it's early end as chewing material.

Professor Fox walked over and examined Arkee's bundle just as she found her mistake. He recognized the rather high-strung girl from the knight bus, sighing inwardly. He nodded to her as she corrected herself. "Ms. Maldemer, you are in the right class. Simply settle down, relax, don't forget to breath, and I'm sure everything will be fine. Why don't you compare your results with your neighbor?"

Walking around the room, he occasionally stopped by various students, helping them if they were stuck, correcting their mistakes, and re-tying their bundles. "Excellent everyone. Everyone seems to be doing very well. Now I would like you to begin discussing this with your neighbors. Consider this as well: if a bundle of seven is stable, would a bundle of 7 bundles of 7 be stable? Do you think ancient wizards and non wizards realized this trick when they had to carry bundles of objects long distances? Discuss this with your friends and neighbors." He concluded by tapping his wand on Astoria's desk. Soon the number of sticks on everyone's table seemed to multiply by 4. Get together with a friend or two and try tying 7 bundles of 7. Once you are done with these exercises, we will conclude today's class and I will announce homework and house points soon after."

luna turned to her neighbour
"soooo, what are we talking about?"

Professor Fox checked his watch then looke dup at the students. "Okay everyone, I think we've taken all the time we dare. I will see everyone during the next class." He tapped his wand on his desk and all the sticks disappeared. "I will post point totals and homework outside my office door. Please check the bulletin boards. If you want to, read about the numbers 1 and 0 for next class. If you have any quesitons or comments about the points awarded, please see me in my office." Having said that, Professor Fox opened the classroom door and stood there, watching the students exit.