Kay added the information to her notes before raising her hand. "Professor Fox, if I'm not mistaken, you are implying that three solves the discord created in the polarity of two. Am I correct?" She paused and then continued. "I understand that three also has negative aspects and is seen as demonic or unnatural, as there are no creatures in our world who walk upon three legs."

Still a bit hesitant but resolute to ask and have her doubt cleared up before they would go on, Nadia raised her hand again. "Professor, I would like to ask something. You previously said the wand core and material made the two component of the wand, when giving an example of the properties of said number. But, wouldn't the lenghts of the wand count for anything? And if so, it should be more an example of the three number?"

"Sure, the lenght isn't a material component," she hastly added, feeling hot all around her face, "but it is somewhat of an important characteristic, I mean to say... well, the lenght is a number, and it would also have some significance, of course, that's what we are learning here, the importance of numbers, no?"

Oh dear, she had completely mixed the tense and surely messed up. Guess the growing reputation of the professor was doing something for her nerves. She bit her lip.

Erica raised her hand and addressed the professor and the class in general.

"I find it interesting that the number 3 is considered the lucky one when muggles usually refer to the number 7 as being lucky. Is there a reason for this? Are the two numbers related in that sense or is that just a muggle thing?"

Professor Fox smiled lightly, "Yes Ms. Black, exactly. We do use arithmancy in our everyday magic. From the simple levitation spells to the 'sideways-walking jynxes' that were quite popular when I was a student, arithmantic properties and prime properties go into each and every spell and magic you young witches use. Thus, an understanding of Arithmancy and how the numbers relate to one another, and the limits and benefits and draw backs of each number go a long way in understanding and formulating magic." He nodded and continued, "That however will be developed in later classes and can get rather complicated, so it is not something one simply looks up. Any other questions or comments?"

"Professor, do you think you could elaborate on how the number 3 is used in house elf magic. Is their magic really that different than ours?"

Professor Fox seemed somewhat jovial, the students were finally getting interested in the subject. "Ah yes, excellent excellent questions each one of you. One at a time, one at a time." He sighed and began pacing behind the desk, holding his glasses and making small hand gestures while answering.

"First of all, Ms. Harrison, the 'demonic' aspect of 3 is superstitious, and is actually a relic of two things: its association with house elves, considered lowly creature by most wizards, wrongly I would add; and the inability of early wizarding folk to explain the fact that triangles are the only permanently stable structures. Early wizards you see, often associated things they couldn't explain or didn't fully understand as evil." He nodded reassuringly, "Good point Ms. Harrison."

"As for your point Ms. Arbon, there is a reason why both 3 and 7 are considered lucky. They both belong to the 'lucky primes' group, which is a large grouping of primes generated by complicated elimination methods known as 'sieves'. Though you will notice that 7 has more say, magical and mystic properties than 3. Again, excellent observation."

"Ms. Rey, your point is an example I thought someone would bring up. If you notice however, the wand core is an external aspect of the wand. That is, the physical wand is made, and then the core is inserted using a series of magical spells. The physical wooden wand is the 'natural' aspect, the core is the 'supernatural' aspect, to borrow a term from non-wizards. So, the length and wood type and what have you are folded into the 'natural' aspect. Good question. Excellent, excellent quesitons everybody."

"Ahh.. Ms..." He leaned over and checked his chalk board, "Ms. Weasley. Well, house elf magic is a vastly under-researched area of magic, if one would ask my opinion. It is really one of those inter-disciplinary magics, combining charms, transfiguration, care of magical creatures, and arithmancy, among others. To answer would be an entire seminar in its own right, to even attempt to do the area justice. Suffice it to say for now, house elves' magic doesn't requrie the same sort of dichotomy as ours does... Say... Wizards use the idea of "input-outcome" or "object-effect." House elves however, often percieve the world differently, and thus focus, think about, and cast magic differently, resulting in simply put, different magic. I hope that answered your question for now, as it is all the time I can devote to it I'm afraid."

He looked around the room, "Are there any more before we move on to 5? Or... should we take a break, and reconvene after everyone has had a stretch?" [ooc note: this would mean, reconvening the class tomorrow, to give people a chance to go to sleep, etcetera]

Lily copied the information down as quick as she could then leaned back in her chair exhausted.

Selena leaned back in her chair and just jotted down a few notes here and there.

Nadia nodded and took some notes, quite interested now the subject about demoniac powers of te number 3 was broughts and the house elves and triagle. Actually, it all was quite interesting. Not to mention she was relieved she hadn't make a complete mess to the point of making an unanswerable question.

"Well," Nadia said, popping in again and raising her hand, "I would also like to know why the 3 it is "often associated more with 'thought' and less with 'reality' ". I do have a theory, like with muggle thought: we need something, the opposite of that something and the result of the existance of said oppossites. Hence the problem-solving thing. Oh and I do too want to ask how the number 3 can be applied in astronomy."

Professor Fox nodded and made a gesture for Nadia to lower her hand, "Yes yes Ms. Rey, we will cover things like that in later classes, for now, we are interested only in the properties of the numbers. Thank you for your interest nonetheless." He looked around the room, "Are we ready to move on then?"

Kali copied down some more downs onto her parchment and muttered a small, "Yes, sir."

Professor Fox began writing again on the board, continuing the lesson. "The number 5, is the third smallest prime and is associated with the material world. Five represents the physical aspect of the interaction that humans and all intelligent beings have with the world. Furthermore, because five represents a being's ability to interact with the physical world, five represents the ability of a being to change and shape the world for the better. For this reason, five is also associated with safety and construction." Professor Fox underlined a number of terms on the board: reality, safety, complementary, construction.

"5, you will find, is also the only prime number ending in 5, because as you all know, any number ending in 5 can be divided by 5. For such reasons, the complementary or constructive aspects of spells are often hidden within the performance of the individual spell. Spells with components associated with 5 tend to be charms and transfiguration spells, as it is a necessity for these spells to have a strong affect on the material world. The number 5 is not strongly associated with any specific beings, though phoenixes and griffins often are associated with the number."

Professor Fox looked at the students, "Are there any specific questions regarding the number 5?"

"So 5 means strong magic?"Lily asked weakly.

"No Ms. Black, it is simply associated with the physical world. I can understand where you might get confused though. Are there any other questions?" He asked, watching the students.

Erica hastily pulled out her text of Fantastic Beasts and Where to Find Them and quickly flipped through the pages until she found what she was looking for before raising her hand.

"Could you elaborate as to why phoenixes are associated with this number? I think I could understand why griffins are, them being used by wizards to guard treasure. That would directly relate to the number and it's tendency toward the material world."

Professor Fox nodded and walked over to a blank area of the board, drawing a rather poor cartoonish represntaiton of phoenix, or more correctly some sort of ball with lines coming out of it and what looked like flames around it. "An excellent question Ms. Arbon, phoenixes are rather complicated creatures," he said as he began drawing five points around the phoenix, "As five is a representative of the physical nature of the world, you will find that the Chinese wizard first developed this idea, phoenixes are the very embodiment of the physical world you see." He continued drawing a number of esoteric, meaningless symbols around the 'phoenix', "Now, phoenixes, unlike other creatures do not die. They burn up, then are reborn from the ashes, moving in a continuous cycle and are forever physical. While this is not to say that they don't have non-physical aspects, of course they do, they simply have such a strong connection to the physical world, that they are indeed, an eternal part of it, only leaving it once they wish." He turned and looked at Erica, "Hence it is not the 'safety' or 'complementary' aspect of the number that they associate with, but the 'physical' aspect they more than other creatures associate with. Does that answer your question?"

Professor Fox hurriedly added, "However, I must confess Ms. Arbon, I am largely only trained to make assertions about the theoretical workings of being and creature magic and how it ocmpares to numbers. I've never been terribly good at the actual handling or care of said creatures."

Erica nodded and quickly took down the notes on the blackboard.

"Yes, Professor, it does. Thank you."

Lily wrote as the Professor spoke.Tryin to stay focused but what ever illness she had was makin it very hard.

Professor Fox nodded and walked back to the board. "Very well, we will cover the number 7, and then after you have given some questions and comments, we will begin a few excercises." He turned to the class before continuing, "Can anyone tell me what they know of the number 7? Magical, mathematical, or otherwise. Anyone at all?"

"Well it's the most magical number" Adz started, thinking carefully. "Also the date of my birthday..." Adz giggled under her breath to her neighbour, giggling

Rosa raised her hand. 'well... it's a prime number. and a quite important one, for instance, the week has 7 days.'

Martha's hand begins to cramp as she takes notes from Professor Fox's lecture. She would definitely need to review the material thoroughly before understanding it.

Quote:

Originally Posted by parchment

Name: Astoria Carmen Delatoure' Fletcher
House: Slytherin
Year: 5

Astoria had been quiet the entire time in the classroom. She didn't make the best impression on Professor Fox and she felt that it was time to redeem herself. She stayed quiet and took notes. Her hand was starting to cramp a bit, but she kept writing her notes down to show she was actually interesting in Arithmancy, which she kind of was.

Nadia raised her hand, "The numeral seven is considered the most mystical of all numbers, and that might be because it is the one number which cannot be divided evenly into the circle (360). If you try said division with every other number even number, you get an even number, while if you devide it with 7 you get," Nadia tried to recall and said, "the number 51.428571.

"The dividend from the division of the circle by the number seven is intriguingly close to the outer angle of the Great Pyramid: 51 degrees and 51 minutes."

"Also," she continued, "it's related to the mystical nature of Pi: The number 22 is considered symbolic of a complete circle, or the circle, because this is reflected by the twenty-two letters in the Hebrew alphabet, the twenty-two keys in the Major Arcana of the Tarot (Keys 1 - 21, plus the Fool) and indicating the full circle of experience. The function 22/7, one cycle of human experience divided by the spiritual Seven or Divinity within. This function is the value of Pi; or, the closet to it as can be expressed in whole digits."

Sara jotted down the notes very quickly. Arithmancy was such an amazing and complicated subject and she really liked it. She nodded at the all of the answers to questions. She didn't want to miss a thing. She was about to raise her hand when she realized that her answer had already been told. The number 7 is a prime number so it is magical and it's the number of days in a week.

Sara then raised her hand very tentatively for a question had just popped into her mind. "Professor, was the number 7 chosen to mark a week because of how magical? I don't quite understand."