 # A Math Question

A math question for the most intrepid engineering minds among us: This is a template for a lantern. It is 55" wide and creates a lantern that is 15" in diameter. If I am adjusting the template to create a lantern that is 16" in diameter and has 8, rather than 6 sections, what is the width of the new template and of each of the 8 sections within?

Hi there asasass,

if the template is 55" wide, then it should create
a lantern with a 17.5" diameter - ( 55/ 2*π ). Do you want to check and revise your requirements?

*2 , because that gives you the radius, but yes. First off: We assume that you want the MINIMUM width of the template. Your drawing doesn’t quite show tangential (‘kissing’) ellipsoids, but for the template to be the minimum width, they would be. If this isn’t the case, the answer is ‘infinity’, because you can have as much distance between each of the sections as you want.

Secondly: We assume you’re making a spherical (or sphereoid) lantern - namely, that the ‘equator’ of your template is a circle.

Given those two assumptions, the sum of the distance of the widest points of your ellipsoids must equal the circumference of the circle enclosed by them.

For a defined diameter, d = 16", you have to apply the circumference of a circle - `C = 2*pi*r`. You’ve defined r (d/2), so it’s simple math at that point.

EDIT:: I mixed up your requirement. woops.

How wide are the segments? We must make a third assumption: That you want equal segments.

If your total width is C, and you divide it into 8 equal segments… I think you can do the math on that one.

There’s really not any math to be done here - except for the curve equations for those ellipsoids. But that’s a whole other matter.

EDIT 2: Okay forum, i didnt want italicizing, i’m doing maths here.

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