# Investigation von koch’s snowflake curve

Worksheet on koch snowflake for students (portfolio task) investigation on von koch's snowflake curve to draw von koch's snowflake curve we • start with an equilateral triangle, c1 • then divide each side into 3 equal parts __,__,__ • then on each middle part draw an equilateral triangle • then delete the side of the. Von koch snowflake investigation powerpoint presentation von koch snowflake this is a brief but very interesting look at the von koch snowflake curve after introducing the curve and discussing its generation, the students are simply asked to derive the perimeter formula for nth iteration (after a reasonable prompt in. The koch snowflake - free download as pdf file (pdf), text file (txt) or read online for free. In the koch snowflake, an infinite perimeter encloses a finite area let's investigate the area below notice the second iteration of the koch snowflake above notice that the original triangle (yellow) is still contained in the koch snowflake with three smaller triangles (red) added in the first iteration, and twelve even smaller.

First constructed in 1904 by helge von koch, a swedish mathematician (to construct a koch of the snowflake's edge, known as the koch curve, yield the entire edge of the snowflake (figure 12) investigate the koch snowflake as having an infinitely long perimeter and compare it to a lake or coastal shoreline viewed. The grade 12 mathematics students did the following investigation on number patterns: koch snowflake 1 koch snowflake 2 koch snowflake 3 koch snowflake 7 koch snowflake 4 koch snowflake 5 see, maths does not have to be boring. Key words: koch snowflake, fractals, infinite perimeter, finite area, numerical in- finities and infinitesimals, supercomputing 1 introduction the first fractal curves have been proposed at the end of xixth century (see, eg it has been introduced by helge von koch in 1904 (see [13]) this fractal is interesting because it is.

B proposed needleless electrospinneret based on von koch fractal curves in the current study, a novel tipped needleless electrospinneret was proposed by the authors based on fractal theory the rudiment of fractal theory was established on the basis of koch snowflake, which is a mathematical curve and one of the. This pin was discovered by adele levin discover (and save) your own pins on pinterest. The koch snowflake was discovered by helge von koch (1870-1924) construct the koch snowflake perimeter area level 0 p(0) = a(0) = level 1 p(1) = a(1) = level 2 p(2) = a(2) = level n p(n) (n is an arbitrary positive integer) = a(n) (n is investigate other fractals, and properties of fractals on the world wide web. Fractals aren't actually on the syllabus – but they do offer quite a good opportunity to look at limits, infinite sequences, complex numbers (eg julia sets etc), the relationship between maths and art and so on this video is a fantastic introduction to fractals – looking at how the koch snowflake has.

Mathematical investigations: a collaborative approach to understanding precalculus name: key sequences and series snowflakes in 1904, helge von koch created a special example by repeating, or iterating, a simple geometric pattern the resulting this later came to be known as the koch snowflake curve. The long-term goal of this work is to justify the existence and investigate, via since the koch snowflake curve (the boundary of the koch snowflake billiard the von koch curve (right) the koch curve is decomposed as the union of four pieces similar to the whole curve figure 3 the koch snowflake curve is obtained by. The area of a koch snowflake is 8/5 of the area of the original triangle - http://en wikipediaorg/wiki/koch_snowflake#properties incredible answer great my best guess is that helge von koch himself, being a swede, would have pronounced his family name cook, but i can't say for certain good answer • 17 votes. The koch snowflake (also known as the koch star and koch island[1]) is a mathematicalcurve and one of the earliest fractal curves to have been described appeared in a 1904 paper titled on a continuous curve without tangents, constructible from elementary geometry by the swedishmathematicianhelge von koch.

Key words: koch snowflake, fractals, infinite perimeter, finite area, numerical in- finities and infinitesimals, supercomputing the first fractal curves have been proposed at the end of xixth century (see, eg it has been introduced by helge von koch in 1904 (see [13]) this fractal is interesting because it. Koch snowflake peano curve barnsley fern lindenmayer systems (l-systems ) different “language” a form of string rewiring starts with an axiom and has a set based on the koch curve, described in the 1904 paper “on a continuous curve without tangents, constructible from elementary geometry” by helge von koch.

## Investigation von koch’s snowflake curve

Mathematics hl portfolio omar nahhas class 12 “ib” (c) the koch snowflake is also known as the koch island, which was first described by helge von koch in 1904 its building starts with an equilateral triangle, removing the inner third of each side, building another equilateral triangle with no base at the location where. It was discovered by the swedish mathematician helge von koch in 1904 3 replace each line segment by a zig-zag curve (a generator) made up of four copies of the line segment it replaces, each reduced to one third of the original length repeat the same try investigating the perimeter as the snowflake grows 3.

• Free essay: adrian zwierzchowski 2 ib investigation – von koch's snowflake curve in this investigation i am going to consider a limit curve named after the.
• Area of the koch snowflake the first observation is that the area of a general equilateral triangle with side length a is 1 2 ⋅ a ⋅ 3 2 a = 3 4 a 2 as we can determine from the following picture height for our construction, the length of the side of the initial triangle is given by the value of s by the result above.
• King, b w snowflake curves math teacher 57, 219-222, 1964 knopp, k einheitliche erzeugung und darstellung der kurven von peano, osgood und v koch arch f math u phys 26, 103-115, 1917 koch, h von sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire.

Von koch to create the koch curve, you start out with a line segment of with length of one unit instead of removing the middle-thirds of the line segment as you do in one interesting result we can show is that although the koch curve has infinite length, the koch snowflake encompasses an area that is finite the koch. The koch curve in order to create the koch snowflake, von koch began with the development of the koch curve the koch curve starts with a straight line that is divided up into three equal parts using the middle segment as a base, an equilateral triangle is created finally, the base of the triangle is removed, leaving us. C 2010–2014 by julian fleron, phil hotchkiss, volker ecke, christine von renesse cooperatively in groups, they may often be part of homework, selected investigations may be solved by your teacher for inside koch's snowflake which is the result of the process started in figure 12 after infinitely many. A shape that has an infinite perimeter but finite area watch the next lesson: https:/ / wwwkhanacademyorg/ math/ geometry/ basic-geometry/ koch_snowflake/ v/ area-.

Investigation von koch’s snowflake curve
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