* He was born in Germany on December 11, 1843.
* Koch decided to change his area of study to medicine from natural science, as he aspired to be a physician. * In July of 1867, following his graduation from medical school, Koch married Emma Adolfine Josephine Fraatz, and the two had a daughter, Gertrude, in 1868 * After his graduation in 1866, he worked as a surgeon in, and following his service, worked as a physician in what today is known as Wolsztyn, Poland the Franco-Prussian War * He is a german

* Koch served as an administrator and professor at Berlin University * Koch’s marriage with Emma Fraatz ended in 1893, and later that same year, he married actress Hedwig Freiberg from 1880 to 1890 * Koch suffered a heart attack on April 9, 1910 and never made a complete recovery * On May 27, only three days after giving a lecture on his tuberculosis research at the berlin academy of sciences * Robert Koch died at baeden baeden at the age of 67

His contributions are as follows:
* Anthrax
* Koch’s four postulates
* Isolating pure culture on solid media
* Cholera
* Tuberculosis
ANTHRAX:
Koch is widely known for his work on this disease. He discovered the causative agent for this disease as Bacillus anthracis. Koch discovered spore-formation in the anthrax bacteria, which could remain dormant under specific conditions. However, under optimal conditions, he found that the spores were activated and caused disease. To determine this causative agent, he dry-fixed bacterial cultures onto glass slides, used dyes to stain the cultures, and then observed them through a microscope. Koch’s work with anthrax is notable in that he was the first to link a particular microorganism with a given disease, rejecting the idea of spontaneous generation and proving the germ theory of disease. KOCH’S FOUR POSTULATES:

During his time as government advisor, he published a report in which he stated the importance of pure cultures in...

...19th Century Medicine
RobertKoch (1834)
Koch worked on anthrax and tuberculosis (TB) and developed work of Louis Pasteur. Koch first investigated Anthrax (that affected herds of farm animals and farmers.) In 1868 Davaine had proved that a healthy animal that did not have anthrax could get the disease if it was injected with blood containing Anthrax. Koch developed this work further. Koch found out that Anthrax microbes produced spores that lived for a long time after an animal had died and these spores could then develop into the Anthrax germ and could infect other animals. After this Koch moved on to Germs. In 1878 he identified the germ that cause blood poisoning and septicaemia and developed new techniques to carry out experiments, and devises a method of proving which germ caused an infection. In 1881 he began to work on TB and found the germ in 1882. Koch finally lay to rest belief that ‘bad air’ caused disease. Koch developed right methods to identify germs.
Louis Pasteur (1882)
A producer of vinegar from beet juice requested Pasteur’s help in determining why the product sometimes spoiled. Pasteur demonstrated that physical screening or thermal methods destroyed all microorganisms and that when no contamination by living contagion took place, the processes of fermentation or putrefaction did not take place. ‘Pasteurization’ and this...

...publically published his findings it meant that Koch was able to take and use these ideas.
So this brings me onto my finally person – RobertKoch. Koch was born in 1843 and died in 1910. RobertKoch himself was a very intelligent person and he was the only one of the three that went to a national university and studied to be a doctor, which meant that before this he had a more extensive knowledge of this topic along with studying other doctors that went before him. After reading Pasteur’s work he focused his research team on looking at taking his works on animals and using them on Humans. This worked extremely well as he was the first person to link specific germs to specific diseases. The two biggest killers in the 19th century were cholera and TB (Tuberculosis) and he found vaccinations for both of these along with more vaccinations for things such as rabies and anthrax. By 1900 he and his students had identified 21 germs causing diseases. A massive help to Koch’s discoveries were based on the dye industry which helped him identify different germs.
In my opinion the least significant person of the three would be Louis Pasteur, this I believe is because even though he did make a lot of progress when he disproved miasma and created the vaccine for such things as anthrax and chicken pox. He did not quite make as much of an impact on the medical world as the other two.
The second most...

...
The Koch Snowflake
Math Mock Exploration
Shaishir Divatia
Math SL 1
The Koch Snowflake
The Koch Snowflake is a fractal identified by Helge Von Koch, that looks similar to a snowflake.
Here are the diagrams of the first four stages of the fractal -
1. At any stage (n) the values are denoted by the following –
Nn - number of sides
Ln - length of each side
Pn - length of perimeter
An - Area of snowflake
Mentioned below are the values of these above variables, for the first 4 stages of the fractal.
n
0
1
2
3
Nn
3
12
48
192
Ln
1
Pn
3
4
An
0.57735
0.64150
0.67001
Number of Sides
As the stages of the snowflake progress, each side is divided into thirds, with two equal line protruding from the middle third to form an edge.
I.e – Each straight line -
Becomes this -
Hence now for everyone 1 line, 4 new ones are formed. Hence we can say that there is geometric progression, by the factor 4.
Hence, the formula for the number of sides is
Nn = 3(4)n
Length of Side
The length of the next side is one-third the previous length. This is once again geometric progression.
Therefore, the equation for the nthterm is:
Ln =
Perimeter
The perimeter of any shape = Length of each side x Number of sides
Considering this, the formula for the perimeter can be obtained by multiplying the formulae of the length and number of sides of the fractal.
Hence
Pn = 3(4)n x
Area
The area of every...

...fractal in nature. Fractal or not, patterns give us something more to admire and wonder about.
Introduction
Fractals never fail to fascinate. If you aren't just gazing at their unearthly beauty, you ponder the mathematics behind them... and then you can't help but wonder how such prosaic, unsensational mathematical formulae can give rise to such intricacy. What is it that makes it possible for (to some) a short, ugly equation to generate the exuberant beauty of the Mandelbrot set? Or is it all just in the way our brains are wired?
Fractals are objects with infinite lengths that occupy finite volumes, resulting in a "fractional dimension" that is not 1-, 2-, or 3-D, but a combination of all three, depending on its spatial configuration.
The Koch snowflake is the repetitive procedure of dividing the image into three equal parts and replacing the middle piece with two similar pieces.
Hypothesis
Fractals mimic nature. (true or false)
This is the basic belief of fractals, and a common concept among those who study fractals. In nature, symmetry is often remarked upon. To mimic is to be similar in to a certain object, and in this case, of a lesser proportion. Thus, we would like to propose that fractals may mimic nature.
Definitions
Fractals
1. A curve or geometric figure, each part of which has the same statistical character as the whole.
2. Any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape...

...The Koch Snowflake
The snowflake model was created in 1904 by Helen von Koch. This snowflake appeared to be one of the earliest fractal curves. The fractal is built by starting with an equilateral triangle. One must remove the inner third of each side and replace it with another equilateral triangle. The process is repeated indefinitely. The length of each side is one which will help you determine the perimeter of each triangle. With having the perimeter of each triangle, the height can be determined so the area can be defined. The height must be determined because to use the formula A=12bh to find the area of the traingle, the height must be known. After repeating the process for the triangles, the graph below displays the number of sides (Nn) for each snowflake, the length of a single side (In), the length of the perimeter (Pn) and the area (An). In 0 1 2 3 1 1/3 1/9 1/27 Nn 3 12 48 192 Pn 3 4 16/3 64/9 An 3/4 3/4(1+13) 3/4(1+13+427)
3/4(1+13+427+16243)
The behavior of the graph above proves that each time a new snowflake is formed, the perimeter increases by 49. So, by simply multiplying 49to the area prior to, you will generate the area for the next sequence. When A4 occurs, these are the following results;
In 4 181
Nn 192
Pn 25627
An 3/4(1+13+427+16243+642187)
When A6 occurs, these are the following results; In 6 1729 Nn 3072 Pn 1024243 ) An 3/4(1+13+427+16243+642187+1024177147...

...A Snowy Evening with Robert Frost
Robert Frost once said, “It begins as a lump in the throat, a sense of wrong, a homesickness, a loneliness. It is never a thought to begin with. It is at best when it is a tantalizing vagueness.” (“Poetry Foundation” n.d.). This poem holds a lot of mystery in its meaning which has a variety of interpretations. John T. Ogilvie who wrote, “From Woods to Stars: A pattern of Imagery in Robert Frost’s Poetry” interprets this as a poem about the journey through life. James G. Hepburn who wrote, “Robert Frost and His Critics” took a different approach. He believes this poem to be about the aesthetics and moral action. This poem contains a variety of literary devices that not only describe the scenery but also the scene itself. Despite its critics who believe this poem to be about the scenery and moral action, Robert Frost’s poem is best understood as a journey through life, because its literary design allows many to have interpreted it this way.
“To watch his woods fill up with snow” “To stop without a farm house near/ Between the woods and frozen lake/ The darkest evening of the year.” “The only other sound’s the sweep/ Of easy wind and downy flake.” “The woods are lovely, dark and deep,” (842-843). The description of the woods is seductive because of the rhyme scheme, AABA/BBCB/CCDC/DDDD. Robert Frost has made comments about the form of this poem, “a...

...In each of his poems, Robert Frost uses multiple stylistic devices and figurative language to convey certain theme, mostly having to do with nature, that ultimately show his modernist style and modernist views on life.
In the poem “Mowing,” the speaker of the poem is mowing his field trying to make grass. While doing this, he ponders the sound that his scythe is trying to “whisper” (Frost 26). The poem is organized into two sections: an octet and a sextet. In the octet, Frost mainly focuses on the sound that the scythe is trying to make by using personification of the scythe. The speaker, in the first part, is trying to describe the “whispering of the scythe” (26) as something very abstract and imaginative. However, in the sextet, he completely rejects any idea that is something abstract like “heat” or “silence,” or that it is anything imaginary, such as “elves” (26). At this point in the poem, Frost focuses purely on fact and the reality of the labor of mowing. This realism is shown throughout the whole poem as the scythe represents reality because it is making things healthy and making them grow, much like the labor of love. It is rewarding after hard work is put into it, but it is just merely work. Nothing more, nothing figurative or imaginative or extraordinary. Working in farmland and putting in hard labor is something that is very humble and real, not dream-like or fantasy-like. Frost also uses alliteration with words such as “love” and “laid,” and...

...Born in Cork, Ireland, in the year 1627, Robert
Boyle was born into a very rich family. His
father, Richard Boyle, was the Earl of Cork.
Part of Boyle's success was because he
lived with one of the richest men of Ireland.
Richard Boyle, however, gained his money
through stealing. His mother died before he was
12.
Though he did well at his school initially, when
a new headmaster arrived, Boyle did poorly. His father
removed him from his school, and hired a tutor to
teach him philosophy, French and mathematics.
Though he did well in all of them, he excelled in math.
After some time, Boyle decided to joins the
"Invisible College" as refered to by Boyle. This is where
he discussed different scientific aspects. John Wilkins,
the leader of the Invisible College, offered Boyle to stay
at Oxford, where he could do his expirements as he
pleases.
His Father: Though he did not directly give any ideas and
inspiration, Boyle's success came from his private tutor
that would have been too expensive for anyone else other
than someone of his father's position.
Galileo: When he visited Italy, he learned about Galileo's
struggles with the Church. From this, he grew to respect
him and agree with Galileo's ideas about science's appli-
cation to life.
John Wilkins: Wilkins gave Boyle much of his education
which helped create his interest, and inspiration.
In 1662, Boyle did an expirement involving a
J Shaped tube,...