Chasing Euclid

The Heretic had a friend with astigmatism who was afraid of hallways because he felt like they were closing in on him. To cure himself he decided to measure the walls of a hallway and prove that they were parallel. He knew the Heretic was good with the latest tools so he asked him to set up a mobile laser-based measuring device with mirrors and other optics and a system processor capable of producing the desired result. The Heretic got a piece of string and some chalk and proceeded to do the proof the way the ancient Greeks did it.

Instructions:

• Cut string #1 to width of hall
• Fold string #1 in half twice and mark the folds to establish 4 quarters of the length
• Cut string #2 to the length of string #1 + ¼
• Tie pencils or chalk to each end of sting #2
• Fold string #2 in half and mark the midpoint
• Layout string #2 at a diagonal from one wall to another
• Tape down or tack the midpoint on string #2
• Use each pencil to draw an arc on the wall
• For each arc, cut string #3 to length of the arc at the endpoints on the floor
• Tape down or tack one end of string #3
• Fold string # in half and tape down or tack the midpoint
• Rotate the free end of string across the arc. If the end of the string matches the line, the arc is a perfect semicircle, therefore the walls are parallel

Explanation

• By creating the arcs with string #2, you are creating double napped cones cut in half by the plane of the floor.
• A plane is perpendicular to the axis of the cones will intersect the cone to create a circle (as demonstrated by string #3).
• Two planes that are perpendicular to the same line (the axis of the cones) are parallel to each other.

                                              

The Greek mathematicians didn't need precise measuring tools. They had precise ideas.

Breakeven

If you have a big idea, at some point you are going to want to make stuff, some sort of swag or actual product. (Hopefully you will only be selling something non-material like a ticket or a download.) Regardless of what you make or whether you want to make a profit, you need to know your breakeven point. How many units do you need to sell to offset the costs of each unit (variable costs) and that unit’s share of the overall costs (fixed costs). 

Here’s a tool to make the calculation…

http://www.dinkytown.net/java/BreakEven.html

Here is an explanation of the formulas involved if you want to do it yourself:

http://knol.google.com/k/break-even-education

You can avoid the break-even problem by eradicating the fixed costs. You do this through on-demand ordering. The product is only created when it is ordered. You only pay for the vendors costs (variable) when you make a sale. The downside is the increased cost for your customers and narrow margins for you. Here’s a service that you can use: http://www.cafepress.com

Here is a link to my cafe press store: http://www.cafepress.com/justbeplatypus

The Butter Knife

`Two days wrong!' sighed the Hatter. `I told you butter wouldn't suit the works!' 

`It was the best butter,' the March Hare meekly replied.

`Yes, but some crumbs must have got in as well,' the Hatter grumbled: `you shouldn't have put it in with the butter-knife.'

Go to the kitchen and get a butter knife…a clean one. Make sure you are living with someone who won’t be freaked out about you walking around the house with a butter knife. Go to the book shelf and reach for the second shelf from the top and place the pinky of your right hand on the right edge of the case. Then stretch out your hand and touch a book with your thumb. Pull that book out half way. Stick the butter knife into the pages about half way through. Pull out the book and go to the page with the knife. Scan the text. Somewhere there is a sentence that holds the key to a problem you have been working on this week. Maybe it won’t be apparent at first but if you close your eyes and take a deep breath, it will come to you.

The magic that makes that trick work can be put to use for your idea if you can work its hidden truth.

QRU?

a paper toy named QRU?

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