







Folding a rectangle to preserve the aspect ratio 
20150509 

From Anna: If you fold a rectangular piece of paper in half and the resulting rectangles have the same aspect ratio as the original rectangle, then what is the aspect ratio of the rectangles? Answered by Penny Nom. 





Golden Ratio 
20130826 

From Mark: Please Help. I'm trying to help my Child and I have no clue on this math question.
Rectangular shapes with a length to width ratio of approximately 5 to 3 are pleasing to the eye.
The ratio is know as the golden ratio. A designer can us the expression 1/3(5w) to find the
length of such a rectangle with width 6 inches. Answered by Robert Dawson and Penny Nom. 





Body measurements 
20100406 

From Amirul: Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student.
My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist?
I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index)..
But teacher said that it is golden ratio...so nothing interesting... =(
really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question?? Answered by Robert Dawson. 





Depth to height ratio 
20090326 

From Janet: Is there a formula to determine how deep something (a cabinet) should be based on how tall it is? Answered by Robert Dawson. 





The Golden Ratio 
20090120 

From Vincent: hello, my name is Vince,
I am wondering how the Golden ratio was used by early mathematicians.
What formula did they use to find it? open for anything... thank You! Answered by Robert Dawson. 





Art and Integers 
20080917 

From pamela: how do artists use integers? Answered by Janice Cotcher. 





A sixfold increase 
20071024 

From Fred: If I have $500 and it grew to $3,000, what is the correct description of the increase? Is it a sixfold increase (sextupled), or a fivefold increase (quintupled)?
When I divide $3,000 by $500, the result is six, therefore, a sixfold increase? Answered by Stephen La Rocque. 





A rectangular sheet of paper is folded along the diagonal 
20070901 

From Amit: A rectangular sheet of a paper with dimensions a and b is folded
along its diagonal. What is the area of the overlapped region? Answered by Harley Weston. 





Circumscribing a golden cuboid with a sphere: surface areas 
20070614 

From Ainslie: A golden cuboid is defined as a rectangular prism whose length, width and height are in the ratio of phi : 1 : 1/phi.
Prove that the ratio of the Surface Areas of the golden cuboid to that of the sphere that circumscribes it is Phi : Pi. Answered by Stephen La Rocque. 





Karats 
20070601 

From Lisa: What is the karat count of gold in a bracelet that contains 15g of gold and 5 g of silver? Answered by Penny Nom. 





Is zero a number or a place holder? 
20070409 

From Chris: Is zero a number or a place holder? 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. 





How old would i be in minutes 
20060809 

From Mariah: i would like to know how old would i be in minutes if i was thirteen years old including leap years Answered by Stephen La Rocque. 





Folding a sheet of paper 
20051215 

From Victoria: The current problem is to take a normal 8 1/2 x 11 sheet of paper, take a corner and fold it to meet the opposite corner, and (without actually measuring) produce a formula to describe the result fold/crease. 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. 





Marching legion 
20040424 

From Art: A column of soldiers is 100 meters long. Their sargeant at the rear of the column gives the order to march. The sargeant marches alongside the column to its head and then back to the rear, at which point he gives the order to halt. In all, the column of soldiers has marched 100 meters. How far has the sargeant marched? I say 187.5 meters, but those who teach or who have taught mathematics tell me no. Some say much more and some different. What do you say? 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. 





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. 





Three goldfish 
20010530 

From Nathan: A man has three goldfish. When the youngest goldfish was born, the oldest fish was three times the middle fish's age. Nine years ago the oldest fish's age was the sum of the two other fish's ages. How old are the three goldfish? Answered by Penny Nom. 





Manifolds 
20010514 

From Thierry: Maybe you could help me, because I have serious problems for the translations of an English mathematic word which is "MANIFOLD". It's impossible to have a clear translation in French. Do you have a solution? Answered by Claude Tardif. 





Crown molding mitre cuts 
20001106 

From Jim Tomfohrde: My question has to do with making mitre cuts when installing crown molding. Crown molding is the trim that is put up at the top of walls with one edge on the wall and the other edge on the ceiling. To make a mitre cut on your mitre saw for a 90degree corner you can lay the molding flat on the saw base, set the bevel of the blade to 34 degrees and the mitre to 31.5 degrees (these may be slightly appoximate). Of course depending on which piece of molding you're cutting you will cut one end or the other, or use the left or right end. These angles allow the cuts to line up and form a seamless corner when they're put in place on the wall/ceiling at 90 degrees. My question is this  is there some mathematical formula from which the 34 degrees and 31.5 degrees are derived. I want to know this because in many cases the corner is not 90 degrees but can be more or less, and in these instances I would like to know if I can calculate the bevel and mitre to use based on the angle of the corner. Answered by Harley Weston. 





Folding a page 
20000301 

From Krista Bischoff: One corner of a page of width a is folded over and just reaches the opposite side. Express L, the length of the crease, in terms of x and a. I can't get the picture to copy to this form so I guess I will have to try and describe the picture the best that I can. The top right hand corner is folded to the left side, almost half way down. The width of the paper is a ( the width of the bottom part which is not folded.) The creased side is L and the part shorter part of the folded area is x (the part that would have been the top right of the original piece.) Answered by Chris Fisher. 





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. 





What is the golden section? 
19950917 

From Cindy: What is the golden section of a line? Answered by Denis Hanson. 





La conjecture de Goldbach 
20110218 

From ahmedbenmoussa: montrez que tout nombre entier paire supérieur à 4 s'écrit somme de deux nombres premiers Answered by Claude Tardif. 





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. 

