







60% as much as $30. 
20140718 

From Kenneth: Question from Kenneth:
Hello:
Do you know why some "as...as" phrases indicate multiplication?
For example, ? is 60% as much as $30. This is equivalent to 60% X $30 = $18. How does this make sense?
I saw this example in an old textbook on business mathematics, but the author did not explain why it is equivalent
to multiplication.
I thank you for your reply. Answered by Robert Dawson. 





An error in finding the mean 
20130225 

From Abhishek: Mean of 50 observations was found to be 80.4 but later all it was discovered 96 was mistake at 69
Find the correct mean? Answered by Penny Nom. 





What was the class average? 
20120420 

From olwale: a class which consist of 15 boys and 10 girls sit for a test. the average score of the boys is 20 and the girls' is 25. find the average score of the class. Answered by Penny Nom. 





The same mean but different ranges 
20120114 

From swathi: Frank and Frances work out at their local gym. the mean of their workout times is the same: 48 min. however, the range of Frank's workout times is 7 min, while the range of Frances'sworkout times is 16 min. explain how this is possible. Answered by Penny Nom. 





Mean and Average 
20120103 

From john: what is the difference between average and mean Answered by Robert Dawson. 





The average age of 300 cars 
20111122 

From Jason: I have 300 used cars built from 1970 to 1980, I would like to know the average
age by total volume. If I provide the qty built per year, can I determine the average age of the lot (300) by total volume?
Total built 
50 
56 
30 
10 
30 
25 
64 
9 
12 
14 
Year built 
1971 
1972 
1973 
1974 
1975 
1976 
1977 
1978 
1979 
1980 
Thanks Answered by Penny Nom. 





The median is greater than the mean 
20090814 

From Shawna: If the median is greater than the mean on a set of test scores, describe the situation. Answered by Robert Dawson. 





Mean 
20090502 

From debra: a hot dog sales per week monday, 100 = tuesday,87 = wednesday, 95 = thursday, 125 = friday, 210 = saturday, 250 = sunday, 57 = what is the mean sales per day? Answered by Penny Nom. 





Zscore 
20090325 

From Barb: I am having trouble finding information on a z score and the conversion to the number of standard deviations a z value can be away from the mean.
What exactly does that mean and what am I looking for?
Help Please. Answered by Harley Weston. 





4 times as many or 4 times more? 
20090202 

From Jackie: Given : Here are 3 squares and 4 sets of 3 circles.
I wonder it is right to write in the below manner to represent the following Conclusion that
can be made from the above given information:
 There are 4 times as many circles as there are squares,
 There are 4 times fewer square than circles;
 There are 4 times more circles than squares.
 ...
Jackie Answered by Robert Dawson. 





Finding the Raw Score for a Mean of 0 and Standard Deviation of 1 
20081002 

From Anita: A variable Y has a distribution of mean of Y =80 and standard deviation of Y=36. Find the values of A and B for transforming y*=A +BY so that mean of y* =0 and standard deviation of y*=1. Answered by Janice Cotcher. 





The average height of an attic 
20080912 

From oliver: I need to find out the average height of a specific volume/area.
a standard house shape side walls height 10m, height in centre of house 15m.
width 15m length 25m (the roof spans the width)
Within the house in the corner there is a (box shape) room which is 5m in height by 3m wide and 4 m long
How do i work out the average height of the space directly above the room (same floor area)? Answered by Stephen La Rocque and Harley Weston. 





What will be the resulting average? 
20080905 

From jean: the average of 9 is 54.if 84 and 90 are added to the set of numbers ,what will be the resulting average? Answered by Penny Nom. 





zscore 
20080702 

From Candace: If a normalshaped distribution has a mean of 80 and a standard deviation of 15 what is the zscore for M=84 for a sample of n=25 scores. Is this sample mean in the middle 95% of the distribution? Answered by Harley Weston. 





The distribution of sample means 
20080702 

From crystal: A population forms a normal distribution with a mean of 75 and a standard deviation of 20. How do I sketch the distribution of sample means for samples of n= 100? Answered by Harley Weston. 





The mean, the median and the mode 
20080623 

From Crystal: Hi my name is Crystal,
My question is
under what circumstances will the mean, the median, and the mode all have the same value? Answered by Stephen La Rocque and Harley Weston. 





The mean and variance 
20080605 

From Donny: An investment will be worth $1,000, $2,000, or $5,000 at the end of the
year. The probabilities of these values are .25, .60, and .15, respectively.
Determine the mean and variance of the worth of the investment. Answered by Harley Weston. 





The average rate of change 
20080329 

From Tom: For the function x/3x1 find the average rate of change between the interval x=1 and x=5? Answered by Harley Weston. 





Expected value and standard deviation 
20080319 

From Patrick: Heres a question i cant figure out:
a small airline company has only three flights per day. The number of
delayed flights per day is regarded as a random variable, and I'm
supposed to calculate the expected
value and standard deviation of the number of delays.
the probability distribution looks like:
No. of Delays: 0 1 2 3
Prob. of delay: 05. 0.3 .1 .1 Answered by Harley Weston. 





Average and mean 
20080317 

From A student: Mean and average are the same propeties of the set of elements, if there is average then why mathematician need the mean ? Answered by Penny Nom. 





Stacks of blocks 
20080207 

From Tammy: i need help for my son he is given 3 stacks of cubes. the 1rst stack has 3 the 2nd stack has 2 the 3rd stack has 4
the question is draw the stacks of cubes so they are arranged correctly to find the mean. what is the mean of the data? Answered by Stephen La Rocque and Penny Nom. 





Mean and standard deviation 
20071210 

From Jamie: Let n be any odd whole number.
a) Which has the greater mean: the odd whole numbers from 1 to n, or the even whole numbers from 2 to n1?
b) Which has the greater standard deviation: the odd whole numbers from 1 to n, or the even whole numbers from 2 to n1? Answered by Penny Nom. 





How old is the 11th person? 
20071208 

From Jamie: Ten people are in a room, and their mean age is 15. After another person enters the room, the mean age is now 18. How old is the person that walked in? Answered by Jesse McLeod and Stephen La Rocque. 





A decision based on data 
20071204 

From manny: You have administered a standardized test of manual dexterity to two groups of 10 semi skilled workers. One of these two groups of workers will be employed by you to work in a warehouse with many fragile items. The higher the manual dexterity of a worker the less likelihood that worker will break significant inventory. Because of a unique contract you must hire all 10 employees from one of the two groups and none of the employees from the other.
You must decide which group to choose. Choose at least two measures of central tendency and at least one measure of dispersion for each group and use those to make your choice. Be sure to justify your choice with at least one page of discussion and analysis. Answered by Penny Nom. 





Grouped data 
20071008 

From Nimra: The following sets of data represent the distributions of
house prices in the northeast and southwest of a country.
Random samples of 100 houses were selected in each region.
(a) Calculate the mean, median and standard deviation for Answered by Harley Weston. 





Finding a geometric mean and taking its antilog 
20070827 

From Jack: Would like to know the basic geometric mean calculation. Also how would I take the antilog from this number? Answered by Stephen La Rocque. 





The change in an average 
20070819 

From farah: the average height of a group of 25 students goes up by 2 cm when astudent of height 165 cm replaces a student from the group.what is the height of the boy who went out of the group? Answered by Stephen La Rocque. 





What was the average? 
20070808 

From Leroy: A total of 50 juniors and seniors were given a math test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test? Answered by Penny Nom. 





A statistics example 
20070802 

From Claudia: A particular employee arrives to work some time between 8:00 am  8:30 am. Based on past experience the Company has determined that the employee is equally likely to arrive at any time between 8:00 am  8:30 am.
On average, what time does the employee arrive?
What is the standard deviation of the time at which the employee arrives?
Find the probability that the employee arrives exactly at 8:12 am?
Find the probability that the employee arrives between 8:20 am  8:25 am? Answered by Har. 





The "mode" of a set of numbers 
20070606 

From Anthony's mom: we have a graph: Kindergarten has 1, 1st has 5, 2nd has 4, 3rd has 3
is the mode "1st grade" because there are more children in that grade? Answered by Stephen La Rocque. 





How to increase your average 
20070524 

From Janna: after taking 4 quizes your average is 71 out of 100. what must your average
on the next 5 quizes be to increase your average to an 81 out of 100? Answered by Penny Nom. 





Normal distribution 
20070524 

From Paula: Consider a data set that is normally distributed.
The mean of the data set is equal to 10,000.
a.) Suppose that, for this data set, 10,625 has a
"zvalue" = 2.5. Solve for the standard deviation of
the data set.
b.) Solve for the "zvalue" of 9,900. Answered by Penny Nom. 





Average 
20070506 

From michelle: the average of x and y is 20. If z = 5, what is the average of x, y, and z. Answered by Stephen La Rocque. 





I have N data points in mdimensional space 
20070429 

From Sid: Hi,
Given below is the problem that I am facing:
I have N data points in mdimensional space. I know the mean euclidean distance of the points from one given point (say the origin). Now I wish to find the mean Euclidean distance of the N points from another given point. How can i do this without knowing the values of the N points and only knowing the 2 origin points and the mean distance from one of the origin points ? Answered by Penny Nom. 





Can you have median < mode < mean? 
20070411 

From Kaliela: Can the Median > mode > mean?
Can the Mean > Mode > Median?
I don't think either of these can occur but I'm unsure why? Answered by Penny Nom. 





Arithmetic means and geometric means 
20070404 

From Dani: Hi!
I was just wondering why the arithmetic mean of sets of numbers is larger than the mean proportional of the same numbers?
Thanks!
Dani Answered by Haley Ess. 





A missing observation 
20070402 

From destinee: please help me my problem is 5,11,19,3,15,17,5,n find n given the following info.range:16 mode:5 median:8 mean:10 what the heck is the answer Answered by Penny Nom. 





The name of an equation 
20061113 

From Lee: I am struggling to find the name of the following equation. I remember watching a TV programme introduced by Arthur C Clarke. The programme focused on an equation that gave a wonderful pattern that went on into infinity. Two maths professors discussed this equation.It was described as 'Gods equation' as it was compared to the shape of trees and other shapes in nature. It was named after the inventor/discoverer. If you have any ideas i would be most grateful. Answered by Penny Nom. 





The median 
20060926 

From Sam: How do you find the median in a group of numbers? Answered by Stephen La Rocque and Penny Nom. 





Absolute Value vs. Standard Deviation ? 
20060424 

From Sonia: Why we don't just take the average of the absolute value of difference scores (use the mean deviation) to describe variability instead of calculating the standard deviation? Answered by Claude Tardif. 





Divide the product of three consecutive positive integers by their mean 
20060312 

From Sandy: When I divided the product of three consecutive positive integers by their mean, I got 99. What is the smallest of the three numbers? Answered by Stephen La Rocque. 





The meaning of numbers 
20060303 

From John: I'm having a philosophical debate on the meaning of numbers, equations, or the world of math in general. Would it be possible if you could help me by giving me a resource that talks about it or if you have your own opinion I would be most grateful. Answered by Harley weston. 





Mean and average 
20051222 

From Jerry: This is just a question from a degreed engineer that has a "understanding" problem. please go to http://www.metrika.com/3medical/hemoglobinm.html
At the end of the page they talk about "mean" vrs "average" there does appear to be a difference. What is it?
Answered by Harley Weston. 





The Mean Value Theorem 
20051222 

From Candace: Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Find all numbers "c" that satisfy the Mean Value Theorem. 11. f(x)=3x^{2} + 2x +5 [1, 1] Answered by Penny Nom. 





Means of sample means 
20051012 

From Fareeha: A population consists of six numbers 1,2,3,4,5,6
a) How many different samples of two numbers can be selected with replacement? and list them.
b) Calculate the mean and standard deviation of the population
b2) Calculate the mean and standard deviation of the mean of the samples.
c) Find the standard error of your estimated mean in question b2 and compare with the estimated standard deviation in b2. Answered by Penny Nom. 





The golden ratio 
20041231 

From Cristina: let x represent the longer segment. to find the golden ratio, write a proportion such that the longer of the two segments is the geometric mean between the shorter segment and the entire segment.Use the quadratic Formula to solve the proportion for X. Find the value in both radical and decimal form. Answered by Penny Nom. 





AB/AP=AP/PB 
20031120 

From James: My name is James McBride. I'm having a difficult time with a pre calculus problem, which goes as follows: "show that AB/AP=AP/PB is equal to (1+5^1/2)/2 (one plus the sqaure root of five with the sum divided by two. I can't do the square root sign, sorry.) I have tried to solve for PB in terms of the other varialbles and then work the quadratic equation. THAT DOES NOT WORK!!!! I am befuddled. Please help me. I am a student of secondary level. Answered by Penny Nom. 





X bar 
20031104 

From mary: Remind me what this means:
_
X
Answered by Andrei Volodin. 





Means 
20031028 

From Abdu:
Question: 80,80,84,85,88,92,97,98 The average of the 8 numbers listed above is 88. Of the following which pair of numbers could be removed from the list without changing the average. A. 80 and 97 B. 80 and 98 C. 84 and 92 D. 84 and 97 E. 85 and 92 Answered by Andrei Volodin and Penny Nom. 





Statistics from grouped data 
20031009 

From Rebecca:
I have to use a suitable computer package (ie. Excel) to work out the mean and standard deviation of the following:
Price Range No of Houses No of Houses
£`000 Area 1 Area 2
45 and under 50 4 5
50 and under 55 7 12
55 and under 60 14 16
60 and under 70 19 18
70 and under 80 8 3
80 and under 100 5 2
I have used excel to work out mean and standard deviation before, but not in a more complicated example like this. Any advice on where to start would be greatly appreciated. Answered by Penny Nom. 





The golden ratio 
20030923 

From Phillip: The Golden Section can be made from an equilatereral triangle inscribed within a circle. The Golden Section is achieved by joining the mid points of two arms of the triangle to the circumference. I can prove this by erecting a perpendicular to the line outside the circle, but am interested to see how it can be proved from within the circle. Answered by Chris Fisher. 





The mean house price 
20030910 

From Carol:
Question: I have to find the mean from the following example: Price Range £000  No of Houses  55 and under 60  3  60 and under 65  6  65 and under 70  13  70 and under 80  21  80 and under 100  15  100 and under 130  7  130 upwards  1  I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated. Answered by Penny Nom. 





E(X + Y) and V(X + Y) 
20030710 

From Reuben:
I'm a teacher trying to find a way to make some stats work from first principles. The topic is expectation algebra and it is for the top age level in high school. By using a set of data I can show how the mean is the same as the expected value ie 2,2,3,4,4 is 15 / 5 = 3 also, 2x0.4+3x0.2+4x0.4=3. I can also show this to work for the variance in the same style but using Sum(xmean)^{2}/n and the Var(X) version of squaring x then multiplying by the probability ( all this for random independant samples). Now comes the tricky bit.....when I try to show E(X+Y) = E(X) + E(Y) from setting up two data sets I get it to work only if I add each item from X to each item from Y. However, I can't get it to work for V(X+Y)=V(X) + V(Y) from two sets of data. There must be something missing in my knowledge of how the sets are required to add together or my knowledge of expectation algebra. I am familiar with proofs but still want to show my students that the basic formulae work from groups of data whether done the long way or by use of formulae. Can you help please? Answered by Penny Nom. 





Mean and median 
20030104 

From Jan:
I have a question re: mean and median. I know what the difference is but just need some clarification on when you would use the mean and when you would use the median. Isn't it the case that with a skewed distribution the average (mean) would be higher or lower than the median, but with a normal distribution they would be very similar values? If you have any examples to help explain this that would be greatly appreciated. I am a teacher (of sorts!) and the person who is asking me the question is actually my boss! Answered by Penny Nom. 





Mean, median and mode 
20020908 

From Ramona:
 How do you calculate the mean, median, and mode?
 what are each of their definitions?
Answered by Leeanne Boehm. 





The mean distance travelled 
20020607 

From A student: If Rosalia travels 1000 km Sheree travels 280 km Daniel travels 50 km Mica travels 200 km Connor travels 500 km Eric travels 250 km Hillary travels 300 km What was the mean distance travelled? How do you arrive at the answer? Answered by Penny Nom. 





The average of two averages 
20020522 

From RJ: in a class with 22 students, the average garde on an exam was 68%, in another class with 32 students, the average grade on the same exam was 78%, what was the overall for the two classes? round your answers to the nearest whole number. Answered by Leeanne Boehm. 





The Dugout, Don's Basement, Cd Corner,... 
20020430 

From A student: The Dugout, Don's Basement, Cd Corner, Harry's Deli, Bill's Software, Anne's Footwear, and Joanne's House cleaning. The gift certificates are each in multiples of $5. There is a $100 range in the value of the gift certificates, which start at $25. The mean value of all seven gift certificates is $80, and the median and mode are both $70. The certificate from The Dugout is worth the most and the one from Joanne House cleaning is worth the least. The total value of the gift certificates from CD Corner, Harry's Deli, and Anne's Footwear is $270, but Anne's Footwear certificate is worth $50 more than the one from Harry's Deli. The Cd Corner gift certificate is equivalent to the mean for this group of three. What is the value of the gift certificates from each store? Answered by Penny Nom. 





Number conversions and averages 
20020203 

From A student: A table has the measurements of 1.6m by 2m, how much material is needed to cover table? I converted to cm then multiplied but got an answer of 32000cm ,so I divide by 100 to get to metres  the answer was 320 which I know is wrong  please explain!! Also I need to explain in my own words what an 'average' is and I am struggling. Answered by Penny Nom. 





Mathematical & conventional meaning of a word 
20011012 

From A student: What is the mathematical & conventional meaning of a word? Like the word Rational or Median. Answered by Penny Nom. 





Ciefficient of variation 
20010923 

From Carmen: I have a question from my OAC finite class. I've come across a problem with the coefficient of variation. I have taught my students that there are no units for coefficient of variation and it can be expressed as a percent. So, for example, a set of data with mean of 5 and standard deviation of 100 would have a CV of 5%. But what happens in this situation: the mean is 4meters and the standard deviation is 0.7mm. Is the CV 1.75% or 0.00175% or 0.0175%? I've had some students change leave the units as is, change them both to mm or change them both to meters...so which is it and why? Answered by Penny Nom. 





The Mean Value Theorem 
20010723 

From Corrie: I need to find if the mean value theorem exists. and if so, find all values c guaranteed by the theorem. f(x) = x^{2}25 on the interval [10,0] Answered by Harley Weston. 





Comparing means and standard deviations 
20010711 

From Shelly: Is there a way to compare means and standard deviations that come from different size samples? Is there an equation that can normalize sample size? Answered by Andrei Volodin. 





The average value of a continuous function 
20010508 

From Esther: The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Answered by Harley Weston. 





Lots of coins 
20010426 

From A student: I purchase 2 million coins at 9.75 I purchase 1 milion coins at 8 what is the formula to calculate my average cost? Answered by Penny Nom. 





A few problems 
20010422 

From Carol: Hello I am a College student trying get through my elmentry concepts class. I am also working with the middle and elementry school student with their work. I was given a few problems to work on and i am having a hard time explaining them to students. DO you think you can help with a coupld of these questions! Answered by Penny Nom. 





8, 4, 2, 18, 1, 9 
20010111 

From Neyra: Place each number below in one of the blanks to create the most meaningful and realistic story possible. Answered by Claude Tardif. 





What is the difference between Mean and Average? 
20001213 

From Julie: What is the difference between Mean and Average? My thinking is the average, is the equal to the sum of all numbers divided by the number of numbers added together. But the mean, I think should be calculated by adding the largest and smallest numbers in the set and them dividing by 2. (which is the point where 1/2 the numbers are higher and 1/2 the numbers are lower) Answered by Patrick Maidorn and Penny Nom. 





Two more problems 
20001201 

From Michael: first question: The mean of three test grades is 74. What must a fourth grade be to increase the mean to 78? final question: The product of two consecutive odd positive integers added to their sum is 119. What are these two integers? Answered by Claude Tardif. 





Expected number 
20001102 

From James: 1)There are 40,25,50 students in the traditional,reformed,and reformed traditional Calculas sections taught by three teachers. On one fine day the three sections congregate together to watch the NOVA video tape on Fermat's Last Theorem. a) A student is randomly selected from he crowed of students.What is the expected number of students in the same section of this student? ****this question which i did not have any idea to do as follow for the part b b) If one of the three teachers is selected at random, what is the expected number of students taught by is teacher? Answered by Harley Weston. 





Mr. Edgecomb's math exam 
20000917 

From Rachel: In Mr. Edgecomb's math class, 30 students took an exam on statistics. If the average passing grade was 84, the average failing grade was 60, and the overall average was 80, how many students passed the test? Answered by Penny Nom. 





Central Limit Theorem and Law of Large Numbers 
20000626 

From Jonathan Yam: The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed. The Law of Large Number states that when sample size tends to infinity, the sample mean equals to population mean. Is the two statements contradictory? Answered by Paul Betts and Harley Weston. 





Sample variance 
20000416 

From Jonathan Freeman: I was just reading your article entitled "A Note on Standard Deviation" I'm now teaching a unit on s.d. and my students were wondering why one uses a denominator of n for a population and n1 for a sample. I saw in your article that this is because "[the quantity] tends to underestimate sigma... and other technical reasons." To which my students again asked... "Why?" Could you please elaborate a bit on the "other technical reasons" perhaps in terms a high school senior (or their teacher...) could understand? Answered by Harley Weston. 





Algebra 
20000118 

From Candis: I want to know what exactly is Algebra? Not how to do it, or methods. Just what is it? Answered by Allen Herman. 





Absolute value 
19991229 

From Alex Waller: What are some practical applications for absolute value? Answered by Harley Weston. 





Fibonacci Numbers 
19991215 

From Gary Nelb: I'm doing a project on fibonacci numbers and I'm using different starting values and finding out if different starting values to see whether or not the ratios still get closer to phi. I was wondering, what numbers should I use. Should I use two of the same # like 2 and 2, or numbers like 1 and 2, or even something totally different. Answered by Denis Hanson. 





Advanced Calculus 
19991207 

From Kay: Hi, my name is Kay. Please helpthese problems are driving me crazzzzy!!!! Your help would be greatly appreciated!  Let a,b be contained in R, a
 .
. . Answered by Claude Tardif. 





Mean, median and mode 
19991207 

From J William Morning: Using the data values 2,2,10,6,5, determine the median, mode and mean. Answered by Penny Nom. 





The sixth game 
19991116 

From Stephanie Sprunger: Janice scored 18,21,27,16,and 19 points in five basketball games. How many points must she score in the next game to raise her average to 22 points per game? Answered by Penny Nom. 





Estimating the population mean 
19991113 

From John Barekman: Statitistics: Estimating the population mean when the standard deviation is known: I am not sure which n to use in the formula for the confidence interval equation: x +/ z*(standard deviation/sqrt(n)) If we have data of ten people, and if we have the data of ten sets of ten people each, what is the difference in the n that we use? What is the difference between the standard deviation and the standard error? Are we using the number of sampling means or just the number of samples? Answered by Harley Weston. 





Mean, median and mode 
19991106 

From Rick: I have five number places and the mean and median are both "0". The mode is greater than the mean. The sum of the absolute values of all of the numbers is 20. The smallest number is 4 less than the next smallest number. What are the five numbers. (negative integers can be used) All of the numbers are integers. Answered by Penny Nom. 





Prime dates 
19990325 

From Jessica Brown: I'm asking how do you figure out all the prime numbers in a year and, whats the average amount of prime numbers per week. Answered by Jack LeSage and Penny Nom. 





Mean and Standard Deviation 
19980422 

From Kit: i have a problem of maths. i think the level of the question is secondary. question: Find the mean and the standard deviation of the numbers:1, 3, 4, 5, 7. i hope u solve this question. thank you so much! Answered by Harley Weston. 





The normal distribution. 
19970321 

From Donna D.Hall: I am looking for a proof for the normal distribution. I suppose "proof" was not a good choice of words. What I am looking for is a way to "derive" the normal distribution in simple terms so that the most average teenager can see the logic. Can you help me? Answered by Harley Weston. 





Nombre d'or 
20031031 

From Claude:
Comment démontrer que si a/b est égal au nombre d'or alors a+b/a est égal aussi au nombre d'or Comment faut t il choisir a et b pour que le puzzle de lewis caroll soit réalisable? on sait déjà que les nombres 8 et 5 ainsi que 6 et 3 ne sont pas valables. Answered by Claude Tardif. 





le nombre d'or 
20000614 

From Belhaj Saad: quel est le nombre d'or? Answered by Claude Tardif. 

