







An open ball is an open set? 
20160623 

From Aqeel: Theorem: The open ball is an open set? Answered by Harley Weston. 





Travelling in a spacecraft 
20160325 

From julie: if i was travelling in a spacecraft at the speed of light and i turned on my headlight would i see the beam ? Answered by Robert Dawson. 





The line of intersection of two planes 
20151209 

From Rabz: Determine the vector equation for the intersection between the two given planes
2x+7y equal to 14,x+z equal to 7 Answered by Penny Nom. 





A region described by inequalities in cylindrical coordinates 
20150221 

From Rahul: I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system)
0=
I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length.
It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!
Regards,
Rahul Answered by Penny Nom. 





An equilateral triangle with vertices in 3 parallel planes 
20140531 

From prajay: How to construct an Equilateral Triangle whose vertices lie on three
parallel lines, if the distances of two lines are 'a' and 'b' units
from the middle line.What is the length of the side of the
Equilateral Triangle ? Answered by Chris Fisher. 





If x+y+z=1 then x^2 + y^2 + z^2 = ? 
20140430 

From Nitin: If x+y+z=1
then
x^2 +y^2+z^2 = ? ? Answered by Robert Dawson. 





A curve in 3space 
20130214 

From pardeep: we have to show that the curve r(t)=(cos t)i+(sin t)j+(1cos t)k ,0<=t<=2pie;
is an ellipse by showing it to an intersection of a right circular cylinder and a plane.
i got the eqn. of the cylinder but did not get the eqn of plane. Answered by Harley Weston. 





A spaceship playhouse 
20100726 

From Dave: I would like to build a spaceship playhouse for my grandson I want it to
be about 36" around and I want to use 5/4 decking boards that measure
5 1/2" wide how do I figure out how to lay out a base pattern to nail to
(what angle do I need to cut and how many boards will it take to go around
the circle. Answered by Penny Nom. 





The triangle inequality 
20100111 

From Nazrul: If A and B are any two vectors, then how can I prove that magnitude of (A+B)<=magnitude of A+magnitude of B. Please show me the process in details. Thank you. Answered by Robert Dawson. 





Elliptic space 
20090918 

From Htet: What is elliptic space and geometry? Answered by Robert Dawson and Chris Fisher. 





Vector spaces 
20090705 

From Nazrul: How can I prove that m(a+b)=ma+mb where a and b are two vectors.
Thank you. Answered by Harley Weston. 





InfiniteDimensional Spaces 
20090626 

From Justin: Hello again, I was also just wondering (in Hilbert Space and Function Space) are there infinitedimensional spaces larger than each other in terms of cardinality? Thanks a lot for your help again!
All the Best,
Justin Answered by Victoria West. 





5 spades 
20090515 

From Dee: From a standard deck of 52 cards, how many cards would you have to draw, without looking at them , to be absolutely certain (a probability of 1) that you had 5 spades? Answered by Robert Dawson. 





The column space of a matrix 
20090212 

From John: Question from John, a student:
A=
1 1 0 0
1 1 0 0
0 0 1 0
0 0 1 1
B=
1 5 6
1 5 6
0 7 2
0 0 9
Is the space spanned by the columns of A the same as the space spanned by the columns of B? Answered by Harley Weston. 





A cardboard spaceship 
20080831 

From Lee: I am building a "cardboard" spaceship for my 4 year old grandson.
The cabin is a dishwasher box with a cool control panel and elipse shaped
windows.
I really need help designing the cone or"nosecone".
The diameter of the base is 26", 24" tall, with a 6" diameter opening
at the top.
Thank you for the help!
Lee Answered by Penny Nom. 





Parabolic arch 
20071009 

From Nisa: A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose suitable rectangular coordinate axes and find the equation of the parabola.
Then calculate the height of the arch at points 10 feet,20feet,and 40 feet from the center. Answered by Stephen La Rocque. 





Cubic meters, square feet and office space 
20070925 

From Kathryn: Can someone please help and let me know how do you convert 11 cubic meters into square footage? Answered by Steve La Rocque and Harley Weston. 





The ratio of arm span to height 
20070917 

From Chandler: I am doing ratios and I was wondering if... well let me explain first. I have data on the arm span and heights of 10 students including myself now i have my measurements of me are 66inches arm span. and 66 inches height. my second piece of data is 71 inches arm span and 67 inches height now my ratio is 71:67 right? i thought i would need to simplify. but i cant really simplify this ratio and these numbers. what do I do? Answered by Stephen La Rocque. 





Two coplanar lines 
20070821 

From Robin: I am going two show that the two lines are coplanar:
(x5)/4=(y7)/4=(z+3)/5
(x8)/7=y4=(z5)/3
I know I have to find a point that lie on both lines, but dont really get it. Answered by Stephen La Rocque and Penny Nom. 





What is the spacing for spindles? 
20070630 

From david: what is the spacing for spindles? a 12ft railing 17 spindles at 1 5/8in ea Answered by Harley Weston. 





Choosing a bicycle 
20070328 

From Jackie: A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible. c) List the sample space. Answered by Penny Nom. 





The distance from a point to a line in 3 space 
20061029 

From Marie: find the distance from the point (1, 2, 3) to the line x = y = z2 Answered by Penny Nom. 





If a person who weighs 270 pounds on Earth 
20060510 

From Chloe: If a person who weighs 270 pounds on Earth weighs 45 pounds in space, how much would a person weigh in space who weighs 132 pounds on Earth? Answered by Stephen La Rocque and Penny Nom. 





A room with a spa 
20050902 

From Stanley: I have a room that is 12 x 16 feet with an 8 foot diameter hole (spa) in it. How many square feet are in this room? Answered by Penny Nom. 





Vectors in three space 
20041030 

From Jo: I have two questions that I just cannot visulise and dont know how to get started on them..!
1. Ship X is sailing North at 4m/s and Ship Y is sailing due East at 3m/s. A sailor on Ship X climbs a vertical pole at 1/2 m/s. What is the velocity of the sailor on Ship X relative to an observer on Ship Y? State it's magnitude and direction.
Not sure where to start with this one...
2. Show, using vectors, that for any tetrahedron, the segments joining the midpoints of the opposite edges are concurrent.
i know what a tetradedron is, and what I am proving but do I solve simultaneously for a specific case?? Answered by Walter Whiteley. 





A 40% increase in garage space 
20041020 

From Dianna: A bus company recently expanded and no longer has enough room in its garage for all of its buses. Twelve of the buses have to be stored outside. If the company decides to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company own? Answered by Penny Nom. 





A garden space 
20040616 

From Carol: We have a 17' x 19' garden space. If we want it a foot high raised bed, how many cubic yards of topsoil do we need? Answered by Penny Nom. 





Spacing the spindles for a railing 
20030606 

From Jennifer:
Scott is a homebuilder. He builds railings in which he places spindles. Spindles ar evertical posts taht are equally spaced beneath a horizontal bar. Scott would like a mathematical model to help him determine the amount of space to put between each spindle. The railing must follow the following criteria: The spaces between each spindle must be equal except for the ones at either end. Theses spaces are smaller. They are half the width of a spindle less than the other spaces. The number of spindles needs to be minimized since spindles are costly. Help Scott determine what width of space to use between the spindles. Create a mathematical model to determine the width of space between each spindle in termso f the number of spindles. Use an 8' (96") railing that has 2 1/2" wide spindles. Explain your thinking. For safety reasons the maximum width of a space is 4" Generalize you model to determine the width of spaces for total railing of length L and spindle width s Answered by Penny Nom. 





Distance in 3space 
20020816 

From David: The question is: how do I figure out the distance of one object in 3D space to another object in 3D space? I have an object at say x = 5.872, y = 2.876, and z = 7.290; and the other object is at x = 1.129, y = 8.213, and z = 11.127. I have been suggested to use the pythagorean theory on this, but since there are three variables, I don't understand how. Answered by Penny Nom. 





A cone in 3 space 
20020320 

From Matthew: Let C in R^{3} be the cone defined by x^{2} + y^{2}  z^{2} = 0 (A) Let P be the plane described by x + 2z = 1 (i) Find a description of P in terms of two parameters s and t . . . Answered by Walter Whiteley. 





A set of points in space 
20020318 

From Victoria: Describe the given set with a single equation or a pair of equations: The set of points in space that lie 2 units from the point(0,0,1) and at the same time 2 units from the point (0,0,1). Answered by Penny Nom. 





Dual spaces 
20011126 

From Hoda: In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of L^{p} is equal to L^{q}. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of l^{p} is equal to l^{q}. Answered by Doug Farenick. 





The "pi" of a circle in hyperbolic space 
20011119 

From Alex: How can you find the "pi" of a circle in hyperbolic space (or is it the same). I would like to know because our environment is hyperbolic and if the "pi" of hyperbolic space is irrational, it would follow that space is non discrete. I would greatly appreciate any help in this question. Answered by Walter Whiteley. 





A line in 3 dimensions 
20011017 

From Murray: I'm working on a complicated proof and i need the equation for a line in 3 dimensions. Answered by Claude Tardif. 





Commas in numbers 
20010906 

From Mike: When did the Ontario Education system drop the use of commas in large numbers and replace with a space? Why? Answered by Walter Whiteley. 





Shape, symmetry, measurement and space 
20010224 

From Marilyn: I have to write in detail about how young children learn about shape, symmetry, measurement and space. It is not activities I need it is how the children learn. How/why their brain takes it all in Answered by Walter Whiteley. 





Why the change from commas between every 3rd digit, to spaces instead? 
20010103 

From Clarende Duby: Why the change from commas between every 3rd digit, to spaces instead? For example: Three million three hundred thirtythree thousand three hundred thirtythree written like: 3 333 333 instead of 3,333,333? Does it have something to do with standardizing mathematical notation worldwide? Answered by Harley Weston. 





Networks of satellites and linear spaces 
20001208 

From David: Let us suppose some companies have collaborated to place several satellites in orbit. Let us call the set of all satellites that a given company helped place in orbit a network. Finally let us assume the following 4 rules.  There are at least two distinct satellites.
 For each pair of satellites there is exactly one network containing them.
 Each network contains at least two distinct satellites.
 For each network, there is a satellite not in it.
What is the least number of satellites. what is the least number of networks? Answered by Penny Nom. 





5 spades 
20001121 

From Matt: In a standard deck of 52 card how many would you have to draw (without looking at them) to be absolutely certain that you had 5 spades? Answered by Claude Tardif. 





Parking spaces 
20001107 

From Lydia: A parking lot has 4 aisles. Each aisle is about 40 yards long and has parking places on both sides. If a parking place is 3 yards wide, how many cars can the parking lot hold? Answered by Penny Nom. 





Intersection of planes 
19981122 

From Dave Rasmussen: I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Coordinate Geometry. I have been teaching my students to write equations of planes and lines,  to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me? Answered by Walter Whiteley and Harley Weston. 





Espaces vectoriels 
20020818 

From Bacar: Comment montrer que trois (ou plus que trois) sous espaces vectoriels sont en somme directe. Answered by Claude Tardif. 

