Charas-Project
Off-Topic => All of all! => Topic started by: GaryCXJk on February 16, 2008, 03:24:19 PM
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Here are some simple problems, which could easily be solved by either logic or simple Math. I haven’t found them on the internet or in any book, but since they’re so simple, you should be able to find it on the internet. However, it’s more fun to find these out yourself.
These problems can be solved with just one sheet of paper. No other tools may be used unless specified. The spoilers are hints, and should only be used if you don't know how to solve it.
- Fold a sheet of paper in three exact pieces. Use any size of paper.
[spoiler]Hint: try using a right triangle.[/spoiler]
- Fold a square sheet of paper into a regular octagon (a polygon with eight sides).
[spoiler]Hint: you can't use two sheets of paper, but you can simulate it with just one.[/spoiler]
- Fold a (square) sheet of paper into a regular hexagon (a polygon with six sides).
[spoiler]Hint: a regular triangle always has three equally sized sides, and each corner has an angle of 60 degrees. A straight angle is 90 degrees.[/spoiler]
- The A paper format is usually constructed in a way that every time you fold the long side in half, the smaller piece of paper has the same width-height ratio as the unfolded sheet. How can you prove this? You may provide a Mathematical solution as proof, but you should also be able to prove this by just folding.
[spoiler]Hint: know that one side devided by the other side is the same as the other side devided by two times one side.[/spoiler]
- The golden ratio is a constant which has some nice properties. One of the properties is that when applied to a piece of paper, cutting off the biggest possible square from one side leaves a remainder with the same width-height ratio as the original. Create such a piece of paper.
[spoiler]Hint: the golden ratio can be calculated by the equation 1 / x = x - 1.[/spoiler]
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I myself have done all these, so it shouldn’t be impossible. If you are providing the answers, use spoiler tags for text only or hyperlinks for images, so you won't spoil it that easy for people.
Also, if you can't find it out by yourself, use the spoilers! There's no shame in it! But I don't think you should need the hints, since these problems are actually quite simple (I'm not that good in creating difficult problems).
For those who really can't work them out, I've created a file with all the answers. However, only use it if you really don't know how it works, or if you want to check up.
mathproblemsolution.pdf (http://www.multiverseworks.com/garycxjkrandomstuff/mathproblemsolution.pdf)
I've also made a second set of questions for when you're done with the first set. These require you to draw. Make sure you follow the rules per assignment.
- You can easily draw a regular hexagon by using circles of the same radius. Explain how it works, and prove it by using Maths.
[spoiler]Hint: try drawing a circle over another one, where the center is exactly on an edge of the first circle. Also, use graph paper if possible.[/spoiler]
- How can you find the exact center line of a quarter circle? You may not fold it in half, nor can you draw outside the circle. You may use a ruler.
[spoiler]Hint: that however doesn't mean you can't draw inside the circle. Also, try using multiples of five for the radius (like five inches or five cm).[/spoiler]
- How can you find the exact center line of a full circle? The same rules apply as the previous one. The center is marked with a dot.
[spoiler]This works exactly the same as the above, you only need to add some more lines.[/spoiler]
- MEDIUM-HARD: Draw two equally sized circles, where the centers of both of the circles lie at the edge (so that the centers lie at the same distance as the radius is). How can you calculate the area of the intersected area? Prove it with a written explaination, and only use illustrations as support.
[spoiler]Two formulas can be used: π r^2 and 0.5 x base x height.[/spoiler]
- HARD: Do the same as the previous one, but this time add a third one of the same radius, with the center at one of the intersections. How can you calculate the area of the intersected area now? The same rules apply.
[spoiler]This works with the aforementioned formulas.[/spoiler]
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Ack. I still take maths. I'm enjoying a nice break from thinking, thanks.
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These seem more like drafting problems than math.
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The first three can be done without Maths, the last two do need Math to actually complete. Although it helps for the first three to use a little bit of Math and logic.
The second set actually mostly does have the need of Math.
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Originally posted by Moosetroop11
Ack. I still take maths. I'm enjoying a nice break from thinking, thanks.