Explain the different types of polar graphs and their equations. Find sites with images of each. **Hint use google and search the images tab. Images can be pasted into blogger and include the link. You should have different sites.
HEY TAYLOR HERE!!! HERE IS MY ANSWER TO THIS PROMPT!!! One type of polar graph is the circle form. It can only be in these forms r= a cos theta or r= a sin theta. When it is placed on a graph it will look like a circle. The equations can only have one number and that is in the front where a is. http://www.chartwellyorke.com/fxmath/fxgraph.html Another polar graph is the limacans or snail graphs. They are called this because when the a-b part of the equation is less than 1 then it makes an inner loop and forms a snail like shape. The equations are a +/- b sin theta or r= a +/- b cos theta and for both of them a>0 and b>0. When on a graph the cos is similar to the sin only on a horizontal axis. http://tutorial.math.lamar.edu/Classes/CalcII/PolarTangents.aspx Another polar graph is the cardioids. It forms the shape of a heart when it is graphed and its formulas are r=a +/- a cos theta and r= a +/- sin theta. http://www.mathwords.com/a/area_polar.htm Another example of polar graphs are rose curves which form a rose when it is graphed. Its formulas are r= a sin ntheta or r= a cos ntheta where a cannot equal 0 and n is an integer greater than 1. When the integer is even then you would multiply the integer by 2 and if it's odd you leave it the same for when you graph it. http://commons.wikimedia.org/wiki/File:Polar_Graph_of_Rose.png The last polar graph is the lemniscates which when graphed forms the figure 8 or a propeller. Its formulas are r^2= a^2 sin 2theta and r^2= a^2 cos 2theta and a does not equal 2. http://www2.seminolestate.edu/lvosbury/CalculusII_Folder/PolarEquationExamples.htm
THAT IS ALL TILL NEXT TIME JA NE (Ggoodbye in japanese).
This is Nathan with the second blog prompt response for the holidays.
The first kind of polar graph is the circle. There are two formulas: r=acos(theta);r=asin(theta) The formula dealing with cos will create a circle with the left-most edge at the pole. With r=asin(theta) the bottom-most edge with be at the pole. http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif
The second type of polar graph is the limacon, or snail graph. The formula is r=a+bsin(theta). If the ratio of a/b is less than 1, then it will have an inner loop. http://www-history.mcs.st-and.ac.uk/Curvepics/Limacon/Limacon1.gif
The third type is the cardioid. The formulas are r=a+-cos(theta); r=a+-sin(theta). These graphs will look like a heart. http://www.walkingrandomly.com/images/mathematica/cardioid.gif
The fourth type is the rose curve. The formula is r=asin n(theta). If n is an even integer, then the rose will have 2n petals. If it is an odd integer, then the rose will have n petals. http://www.daviddarling.info/images/quadrifolium.png
The final graph is the lemniscate. The formula is r^2=a^2sin2(theta). It has the shape of a figure-8 or a propeller. http://merganser.math.gvsu.edu/david/reed05/projects/kim/msri-jihokim/pics/lemniscate.png
hola. types of polar graphs: circle rose limacon lemniscate cardiod
formulas:
circle-acos(theta);r=asin(theta) rose-r=asin n(theta limacon-r=a+bsin(theta) lemniscate-r^2=a^2sin2(theta) cardiod- r=a+-acos(theta)or same with sin
information circle-is just a circle, "a" is the diameter. rose-if the number before that theta is even, then you double that number and thats how many petals is will have, if the number is odd, that number stays the same limacon-is a/b is less than one, you get an inner loop but other than that, its kinda like a circle. cardioid- THEY LOOK LIKE LITTLE HEARTTSS:) lemniscate-they look like clovers
pictures: http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/anderson/writeup11/writeup11.html i swear this site has it all. check it out.
Circle A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the centre or center. The common distance of the points of a circle from its centre is called its radius.Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. Picture:http://en.wikipedia.org/wiki/Circle Rose In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates. Picture http://en.wikipedia.org/wiki/Rose_(mathematics) Limacon and cardoid a limaçon, also known as a limaçon of Pascal, is defined as a roulette formed when a circle rolls around the outside of a circle of equal radius. It can also be defined as the roulette formed when a circle rolls around a circle with half its radius so that the smaller circle is inside the larger circle. Thus, they belong to the family of curves called centered trochoids; more specifically, they are epitrochoids. The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp. picture:http://en.wikipedia.org/wiki/Lima%C3%A7on lemnicate the lemniscate is a plane curve defined from two given points F1 and F2, known as foci, at distance 2a from each other as the locus of points P so that PF1·PF2 = a2. The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from lemniscus, which is Latin for "pendant ribbon". It is a special case of the Cassini oval and is a rational algebraic curve of degree 4. picturehttp://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli
this is lawrence doing the blog prompt number dos. there are five polar graphs that we learned. they are easy to identify and the formulas are simple too. i liked when b rob had us see which ones were which because i knew them and im sure i passed that part on the exam.
the 5 different types of polar graphs are: circle rose limacon lemniscate cardiod
the formulas are: circle-acos(theta);r=asin(theta) rose-r=asin n(theta limacon-r=a+bsin(theta) lemniscate-r^2=a^2sin2(theta) cardiod- r=a+-acos(theta)or same with sin
circle- explains itself. a is the diameter. rose-if the number before that theta is even then you double the number and thats how many petals it will have, if the number is odd then number stays the same limacon-is a/b is less than one, you get an inner loop but other than that, its kinda like a circle. cardioid- they are heart lemniscate- are clovers
ROSE- r=AsinN(theta) when you graph this is makes a shape that looks like a rose. when A is even, you double that number and thats how many petals the rose will have, but if its odd then that number stays the same.
circle: r = acostheta & r = asintheta for these a is the diameter of the circle. when drawn you get a circle (hence why it's callled a cirlce polar graph) ~~> the picture http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif&imgrefurl
rose: r = asinbtheta & =acosbtheta when graphed the rose polar graph as mulitple little circle things that look like petals. if the a is a even number then the petals double and if a is a odd number the amount petals will be the number of a. ~~> the picture? http://us.monografias.com/docs33/polar-coordinate/Image5617.gif&imgrefurl
Limacon: r = a +/- bsintheta & r = a +/-bcostheta depending on whether a/b is less than one, the limacon has 3 basic shapes. one of which has a inner loop. ~~> picture http://www.mathsdiscovery.co.uk/Flyer1_files/image016.gif&imgrefurl
lemniscate: r^2 = a^2sin2theta & r^2 = a^2cos2theta clover looking things when graphed ~~>picture http://www.mathwords.com/a/a_assets/area%2520polar%2520exampleGraph.gif&imgrefurl
cardiod: r = a-acostheta & r = a-asintheta when graphed these looks like hearts, the pointed heart indention is always in the line of symetry. ~~> the picture http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png&imgrefurl
Tori's... 2 down, 5 to go. the 5 different types of polar graphs are: circle rose limacon lemniscate cardioid
the formulas are: circle-acos(theta);r=asin(theta) rose-r=asin n(theta limacon-r=a+bsin(theta) lemniscate-r^2=a^2sin2(theta) cardioid- r=a+-acos(theta)or same with sin
circle- obviously its shaped like a circle: a is the diameter. rose-if the number before the theta is even then you double the number and thats how many petals it will have, if the number is odd then number stays the same limacon-is a/b is less than one, you get an inner loop. if not, then it just looks like a wop circle. cardioid- they resemble hearts lemniscate- look like the infinity symbol
There are several types of polar graphs: circle-a circle rose-shapes a flower limacon-forms an circle with or without an inner loop lemniscate-forms the infinity symbol cardioid-a heart
My Internet is being stupid and won't load google images...fml.
types of polar graphs: circle rose limacon lemniscate carded formulas: circle-acos(theta);r=asin(theta) rose-r=asin n(theta limacon-r=a+bsin(theta) lemniscate-r^2=a^2sin2(theta) cardiod- r=a+-acos(theta)or same with sin information circle-is just a circle, "a" is the diameter. rose-if the number before that theta is even, then you double that number and thats how many petals is will have, if the number is odd, that number stays the same limacon-is a/b is less than one, you get an inner loop but other
HEY TAYLOR HERE!!! HERE IS MY ANSWER TO THIS PROMPT!!!
ReplyDeleteOne type of polar graph is the circle form. It can only be in these forms r= a cos theta or r= a sin theta. When it is placed on a graph it will look like a circle. The equations can only have one number and that is in the front where a is. http://www.chartwellyorke.com/fxmath/fxgraph.html
Another polar graph is the limacans or snail graphs. They are called this because when the a-b part of the equation is less than 1 then it makes an inner loop and forms a snail like shape. The equations are a +/- b sin theta or r= a +/- b cos theta and for both of them a>0 and b>0. When on a graph the cos is similar to the sin only on a horizontal axis. http://tutorial.math.lamar.edu/Classes/CalcII/PolarTangents.aspx
Another polar graph is the cardioids. It forms the shape of a heart when it is graphed and its formulas are r=a +/- a cos theta and r= a +/- sin theta. http://www.mathwords.com/a/area_polar.htm
Another example of polar graphs are rose curves which form a rose when it is graphed. Its formulas are r= a sin ntheta or r= a cos ntheta where a cannot equal 0 and n is an integer greater than 1. When the integer is even then you would multiply the integer by 2 and if it's odd you leave it the same for when you graph it. http://commons.wikimedia.org/wiki/File:Polar_Graph_of_Rose.png
The last polar graph is the lemniscates which when graphed forms the figure 8 or a propeller. Its formulas are r^2= a^2 sin 2theta and r^2= a^2 cos 2theta and a does not equal 2. http://www2.seminolestate.edu/lvosbury/CalculusII_Folder/PolarEquationExamples.htm
THAT IS ALL TILL NEXT TIME JA NE (Ggoodbye in japanese).
This is Nathan with the second blog prompt response for the holidays.
ReplyDeleteThe first kind of polar graph is the circle. There are two formulas: r=acos(theta);r=asin(theta)
The formula dealing with cos will create a circle with the left-most edge at the pole. With r=asin(theta) the bottom-most edge with be at the pole.
http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif
The second type of polar graph is the limacon, or snail graph. The formula is r=a+bsin(theta). If the ratio of a/b is less than 1, then it will have an inner loop.
http://www-history.mcs.st-and.ac.uk/Curvepics/Limacon/Limacon1.gif
The third type is the cardioid. The formulas are r=a+-cos(theta); r=a+-sin(theta). These graphs will look like a heart.
http://www.walkingrandomly.com/images/mathematica/cardioid.gif
The fourth type is the rose curve. The formula is r=asin n(theta). If n is an even integer, then the rose will have 2n petals. If it is an odd integer, then the rose will have n petals.
http://www.daviddarling.info/images/quadrifolium.png
The final graph is the lemniscate. The formula is r^2=a^2sin2(theta). It has the shape of a figure-8 or a propeller.
http://merganser.math.gvsu.edu/david/reed05/projects/kim/msri-jihokim/pics/lemniscate.png
hola.
ReplyDeletetypes of polar graphs:
circle
rose
limacon
lemniscate
cardiod
formulas:
circle-acos(theta);r=asin(theta)
rose-r=asin n(theta
limacon-r=a+bsin(theta)
lemniscate-r^2=a^2sin2(theta)
cardiod- r=a+-acos(theta)or same with sin
information
circle-is just a circle, "a" is the diameter.
rose-if the number before that theta is even, then you double that number and thats how many petals is will have, if the number is odd, that number stays the same
limacon-is a/b is less than one, you get an inner loop but other than that, its kinda like a circle.
cardioid- THEY LOOK LIKE LITTLE HEARTTSS:)
lemniscate-they look like clovers
pictures:
http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/anderson/writeup11/writeup11.html
i swear this site has it all. check it out.
Circle
ReplyDeleteA circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the centre or center. The common distance of the points of a circle from its centre is called its radius.Circles are simple closed curves which divide the plane into two regions, an interior and an exterior.
Picture:http://en.wikipedia.org/wiki/Circle
Rose
In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates.
Picture
http://en.wikipedia.org/wiki/Rose_(mathematics)
Limacon and cardoid
a limaçon, also known as a limaçon of Pascal, is defined as a roulette formed when a circle rolls around the outside of a circle of equal radius. It can also be defined as the roulette formed when a circle rolls around a circle with half its radius so that the smaller circle is inside the larger circle. Thus, they belong to the family of curves called centered trochoids; more specifically, they are epitrochoids. The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp.
picture:http://en.wikipedia.org/wiki/Lima%C3%A7on
lemnicate
the lemniscate is a plane curve defined from two given points F1 and F2, known as foci, at distance 2a from each other as the locus of points P so that PF1·PF2 = a2. The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from lemniscus, which is Latin for "pendant ribbon". It is a special case of the Cassini oval and is a rational algebraic curve of degree 4.
picturehttp://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli
this is lawrence doing the blog prompt number dos. there are five polar graphs that we learned. they are easy to identify and the formulas are simple too. i liked when b rob had us see which ones were which because i knew them and im sure i passed that part on the exam.
ReplyDeletethe 5 different types of polar graphs are:
circle
rose
limacon
lemniscate
cardiod
the formulas are:
circle-acos(theta);r=asin(theta)
rose-r=asin n(theta
limacon-r=a+bsin(theta)
lemniscate-r^2=a^2sin2(theta)
cardiod- r=a+-acos(theta)or same with sin
circle- explains itself. a is the diameter.
rose-if the number before that theta is even then you double the number and thats how many petals it will have, if the number is odd then number stays the same
limacon-is a/b is less than one, you get an inner loop but other than that, its kinda like a circle.
cardioid- they are heart
lemniscate- are clovers
http://www.google.com/imgres?imgurl=http://www.education.com/files/static/mcgrawhill-images/9780071431194/f0264-02.jpg&imgrefurl=http://www.education.com/reference/article/everyday-math-help-graphing-some/&usg=__YOeXeHgSiEEKU_IEdLrUD_CcHoY=&h=314&w=287&sz=45&hl=en&start=13&zoom=1&tbnid=7zMK2LptOGpm7M:&tbnh=146&tbnw=139&prev=/images%3Fq%3Dimages%2Bof%2Ba%2Bcircle%2Bin%2Ba%2Bpolar%2Bgraph%26hl%3Den%26biw%3D1020%26bih%3D619%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=328&ei=DoAbTcD-LoG78gaj7ZXSDQ&oei=BoAbTZaEFYL6lweYltjICw&esq=3&page=2&ndsp=15&ved=1t:429,r:7,s:13&tx=58&ty=60
http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/f/f5/Polar_Graph_of_Rose.png&imgrefurl=http://commons.wikimedia.org/wiki/File:Polar_Graph_of_Rose.png&usg=__OUKVz42K_QSR5_mMaIVN_LmHfWE=&h=366&w=367&sz=42&hl=en&start=0&zoom=1&tbnid=pCWoknsoS8A9XM:&tbnh=155&tbnw=155&prev=/images%3Fq%3Dimages%2Bof%2Ba%2Brose%2Bin%2Ba%2Bpolar%2Bgraph%26hl%3Den%26biw%3D1020%26bih%3D619%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=hc&vpx=141&vpy=71&dur=906&hovh=224&hovw=225&tx=118&ty=109&ei=LYAbTd6kLcOAlAev2fnPCw&oei=LYAbTd6kLcOAlAev2fnPCw&esq=1&page=1&ndsp=13&ved=1t:429,r:0,s:0
http://www.google.com/imgres?imgurl=http://home.earthlink.net/~djbach/graphs/polar/limacon.gif&imgrefurl=http://home.earthlink.net/~djbach/trig.html&usg=__Yl7LKUfG6eac2JfVbvkhPFHQkrU=&h=99&w=90&sz=1&hl=en&start=0&zoom=1&tbnid=8E2ij9LZ0KBRuM:&tbnh=83&tbnw=75&prev=/images%3Fq%3Dimages%2Bof%2Ba%2Blimacon%2Bin%2Ba%2Bpolar%2Bgraph%26hl%3Den%26biw%3D1020%26bih%3D619%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=266&ei=TIAbTaedCMSqlAeruonICw&oei=TIAbTaedCMSqlAeruonICw&esq=1&page=1&ndsp=13&ved=1t:429,r:3,s:0&tx=43&ty=74
http://www.google.com/imgres?imgurl=http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Perry/Assignment%25201%2520Distance%2520Equations/Distance%2520equations_files/image065.jpg&imgrefurl=http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Perry/Assignment%25201%2520Distance%2520Equations/Distance%2520equations.htm&usg=__2cGY_dh2SpYbjiu1EAitk6k1fsk=&h=293&w=397&sz=16&hl=en&start=0&zoom=1&tbnid=-LrJ99BUAPrg4M:&tbnh=121&tbnw=164&prev=/images%3Fq%3Dimages%2Bof%2Blemniscates%2Bin%2Bpolar%2Bgraphs%26hl%3Den%26biw%3D1020%26bih%3D619%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=406&ei=h4AbTeHHNsL6lwfo2LDACw&oei=h4AbTeHHNsL6lwfo2LDACw&esq=1&page=1&ndsp=15&ved=1t:429,r:0,s:0&tx=108&ty=64
the 5 different types of polar graphs are:
ReplyDelete1)circle
2)rose
3)limacon
4)leminiscate
5)cardioid
CIRCLE- r=Acos(theta) r=Asin(theta)
when you graph this it makes a circle, obviously. the diameter of a circle is A.
http://demonstrations.wolfram.com/PolarAndRectangularCoordinates/HTMLImages/index.en/popup_1.jpg
ROSE- r=AsinN(theta)
when you graph this is makes a shape that looks like a rose. when A is even, you double that number and thats how many petals the rose will have, but if its odd then that number stays the same.
http://upload.wikimedia.org/wikipedia/commons/f/f5/Polar_Graph_of_Rose.png
LIMACON- r=A+Bsin(theta)
its almost like a circle but if a/b is less than 1, then you get an inner loop inside of it.
http://curvebank.calstatela.edu/index/limacon.gif
LEMINISCATE- r^2=A^2sin2(theta)
these look like clovers when you graph them.
http://curvebank.calstatela.edu/index/lemniscate.gif
CARDIOID- r=A+-Asin(theta)
when you graph these, they almost look like a heart.
http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png
Charlie's.
ReplyDeletethere are 5 types of polar graphs.
circle:
r = acostheta & r = asintheta
for these a is the diameter of the circle. when drawn you get a circle (hence why it's callled a cirlce polar graph)
~~> the picture
http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates_files/image006.gif&imgrefurl
rose:
r = asinbtheta & =acosbtheta
when graphed the rose polar graph as mulitple little circle things that look like petals. if the a is a even number then the petals double and if a is a odd number the amount petals will be the number of a.
~~> the picture?
http://us.monografias.com/docs33/polar-coordinate/Image5617.gif&imgrefurl
Limacon:
r = a +/- bsintheta & r = a +/-bcostheta
depending on whether a/b is less than one, the limacon has 3 basic shapes. one of which has a inner loop.
~~> picture
http://www.mathsdiscovery.co.uk/Flyer1_files/image016.gif&imgrefurl
lemniscate:
r^2 = a^2sin2theta & r^2 = a^2cos2theta
clover looking things when graphed
~~>picture
http://www.mathwords.com/a/a_assets/area%2520polar%2520exampleGraph.gif&imgrefurl
cardiod:
r = a-acostheta & r = a-asintheta
when graphed these looks like hearts, the pointed heart indention is always in the line of symetry.
~~> the picture
http://upload.wikimedia.org/wikipedia/commons/6/6d/Polar_pattern_cardioid.png&imgrefurl
http://lpc1.clpccd.cc.ca.us/lpc/math/math2/polar.pdf
Graphs of Polar Equations
ReplyDelete5 Types:
1)Circles
r= acostheta- is where "a" is the diameter of the cirlce that has its left-most edge at the pole.
http://www.uwec.edu/smithaj/Fall2001/216/lectures/images/Oct165.gif
r=asintheta- is where "a" is the diameter of the cirlce that has its bottom-most edge at the pole.
https://www.math.duke.edu/education/prep03/Images/images/maplesamples7.gif
2)Limacons
r=a+/-b sin theta, where a>0 and b>0
r=a+/-b cos theta, where a>0 and b>0
If the ratio a/b is less than one, then it will have an inner loop.
http://newton.uor.edu/facultyfolder/deweerd/research/limacon.jpg
3)Rose Curves
r= a sin n(theta) or r= cos n(theta
If n is an even integer, then the rose will have 2n petals. If n is an odd integer, then the rose will have n petals.
http://www.mathwords.com/r/r_assets/r116.gif
4)Lemniscates
r^2=a^2 sin 2(theta) or r^2=a^2 cos 2(theta)
Kinda looks like a clover when graphed
http://media.photobucket.com/image/lemniscates%20graphed/labasrasa/polargraphs.png
5)Cardiods
r= a+/-acos theta or r=a+/- a sin theta
When you graph it, it kinda looks like a heart
http://www.walkingrandomly.com/images/mathematica/cardioid.gif
Tori's...
ReplyDelete2 down, 5 to go.
the 5 different types of polar graphs are:
circle
rose
limacon
lemniscate
cardioid
the formulas are:
circle-acos(theta);r=asin(theta)
rose-r=asin n(theta
limacon-r=a+bsin(theta)
lemniscate-r^2=a^2sin2(theta)
cardioid- r=a+-acos(theta)or same with sin
circle- obviously its shaped like a circle: a is the diameter.
rose-if the number before the theta is even then you double the number and thats how many petals it will have, if the number is odd then number stays the same
limacon-is a/b is less than one, you get an inner loop. if not, then it just looks like a wop circle.
cardioid- they resemble hearts
lemniscate- look like the infinity symbol
Feroz.
ReplyDelete5 types of polar graphs.
Circle.
Rose.
Limacon.
Lemniscate.
And Cardiod.
I was gonna make a Captain Planet joke but I just forgot it. Oh well, on with this thing.
[Circle]
acos(Θ)
r= asin(Θ)
[Rose]
r= asin n(Θ)
[Limacon]
r= a+bsin(Θ)
[Lemniscate]
r^2= a^2sin2(Θ)
[Cardiod]
r= a + -acos(Θ)
http://www.alamo.edu/sac/slac/pdfs/math2412/grphpeqs.pdf
This PDF has pictures of all them, kinda looks like that packet you gave us awhile back.
There are several types of polar graphs:
ReplyDeletecircle-a circle
rose-shapes a flower
limacon-forms an circle with or without an inner loop
lemniscate-forms the infinity symbol
cardioid-a heart
My Internet is being stupid and won't load google images...fml.
types of polar graphs:
ReplyDeletecircle
rose
limacon
lemniscate
carded
formulas:
circle-acos(theta);r=asin(theta)
rose-r=asin n(theta
limacon-r=a+bsin(theta)
lemniscate-r^2=a^2sin2(theta)
cardiod- r=a+-acos(theta)or same with sin
information
circle-is just a circle, "a" is the diameter.
rose-if the number before that theta is even, then you double that number and thats how many petals is will have, if the number is odd, that number stays the same
limacon-is a/b is less than one, you get an inner loop but other