# Math and optical illusions relationship quizzes

### These 6 Optical Illusions Will Reveal 6 Hidden Sides of Your Personality - The Minds Journal

Recognize and use connections among mathematical ideas. Geometry and Art : Optical Illusions and the Fibonacci Sequence. Idaho Content .. angles quiz. Workouts, Personality Tests, Logical Thinking, Math Tricks Or Optical illusions. We found the best 12 illusions to test your brain, just try to see them from a. Many personality tests rely on your choices to determine your personality, but this Below, you'll find seven optical illusions in which a number of things can be.

While there are similar optical illusions to this one that can be produced and reproduced by human hands, this one is so precise that it must be created with exact measurements, along with a machine that can follow those exact measurements to the millimeter.

It just goes to show that even a child's toy can be used to create some absolutely amazing things. Question 15 Are the white lines the same size?

Yes No While many used this image for years to easily present how perspective can change how our brains perceive the world around us, it was eventually proven to be a fake. Somebody, using camera and photography trickery, was able to manipulate this image and move the train tracks closer together further down the line, thereby increasing the shock when the image was presented. While we all know parallel lines appear closer as they approach the horizon, this image is actually an exaggeration of that phenomenon.

Question 16 How many colors do you see? This both amazes and worries us, as it just once again highlights how unreliable our own bodies are. We really do live our lives under the misconception that this stuff will always have our back, but this sadly isn't the case. However, one of the best things about these illusions is that they can tell us so much about ourselves, which hopefully this will one day too.

Question 17 How many full circles do you see?

## Visual curiosities and mathematical paradoxes

If tie-dye and surrealist imagery are anything to go by, it's quite clear that LSD and similar drugs clearly leave people with the ability to create some mind-bending stuff, this illusion being one of them. As you look at it, the circles appear to be turning, despite the fact that they aren't moving. This was handed out to people to trip them out while they came up on drugs at the infamous festival.

Question 18 Both sides of the image are the same color and brightness. True False Yet another illusion that works with color rather than perspective, this highlights how two of the same color, when placed together can actually appear different due to the way our brain perceives them. If you were to place a thin band of white between these two blocks of gray, it would become immediately apparent they are the same color, but for whatever reason, our brain is unable to see this once they're placed together with a mere dividing line between them.

Question 19 This triangle is actually physically impossible in the world of geometry. True False This image is used by mathematicians to teach students that when it comes to geometry, your eyes and knowledge can be easily fooled. While this image appears to take place over the same number of squares, meaning it shouldn't matter what position the shapes are placed in.

However, if you rearrange the shapes from their original placing, it is possible to end up with a missing square, which should make no sense from what we know of geometry. While there is a solution to this, it continues to stump students to this day.

### Optical illusions Quiz | Personality Test | QuizzClub

Question 20 This is actually a woman's legs made to look like a lamp through photoshop and camera tricks. True False This one has done the rounds on the internet many times and for many years at this point, usually with a headline claiming that what you see the first time you look at this image will tell you whether or not you have a naturally dirty mind, but the truth of it is, an artist actually created this image to show how easily a natural form can be manipulated into something else in the modern world.

Far from dirty minded, you're actually seeing the truth. Question 21 This illusion was created by a band for their first album. True False We may bang on about this too much for some of you, but it's true that art continues to bring us some of the most impressive changes in the modern world.

This is now one of the most impressive modern optical illusions that we have and it came about because a band wanted a cool album cover. Escher used the Penrose triangle in his constructions of impossible worlds, including the famous Waterfall click on the link to see the image. In this drawing, Escher essentially created a visually convincing perpetual-motion machine. It's perpetual in that it provides an endless water course along a circuit formed by the three linked triangles.

The Penrose staircase figure 6 is not a real staircase — it's an impossible figure. The drawing works because your brain recognises it as three-dimensional and a good deal of it is realistic.

At first glance, the steps look quite logical. It is only when you study the drawing closely that you see the entire structure is impossible.

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Escher incorporated the Penrose staircase in his lithograph Ascending and Descending. You can see the lithograph by clicking on the link and you can read more about this in [11]. The Penrose stairway leads upward or downward without getting any higher or lower — like an endless treadmill.

Escher drew his staircase in perspective, which would indicate another size illusion. The monks that are descending should get smaller and the ones that are ascending should get larger.

In this case Escher was prepared to cheat a little bit. At first glance, the steps appear quite logical. It is only when one studies it more closely that one sees the entire structure is impossible. It is arguably the most reproduced impossible object of all time. Another impossible object is the space fork figure 7. One notices in the figure that three prongs miraculously turn into two prongs.

The problem arises from an ambiguity in depth perception. Your eye is not given the essential information necessary to locate the parts, and the brain cannot make up its mind about what it is looking at.

The problem is to determine the status of the middle prong. If you look at the left half of the figure, the three prongs all appear to be on the same plane; in other words, they seem to share the same spatial-depth relationship. However, when you look at the right half of the figure the middle prong appears to drop to a plane lower than that of the two outer prongs. So precisely where is the middle prong located?

It obviously cannot exist in both places at once. The confusion is a direct result of our attempt to interpret the drawing as a three-dimensional object. Locally this figure is fine, but globally it presents a paradox.

Sometimes this figure is referred to in the literature as a cosmic tuning fork or a blivet. Paradoxes, sliding puzzles and vanishing pictures Paradoxes A paradox often refers to an appearance requiring an explanation. Things appear paradoxical, perhaps because we don't understand them, perhaps for other reasons. As the mathematician Leonard Wapner see [12] notes, paradoxical statements or arguments can be categorised into one of three types.

A statement which appears contradictory, even absurd, but may in fact be true. The Banach-Tarski theorem involves a type 1 paradox, since there is a conclusion of the theorem that appears to contradict common sense; yet, the conclusion is true. The result is that, theoretically, a small solid ball can be decomposed into a finite number of pieces and then be reconstructed as a huge solid ball, by invoking something called the axiom of choice. The axiom of choice states that for any collection of non-empty sets, it is possible to choose an element from each set.

This may sound like a perfect solution to your financial troubles, simply turn a small lump of gold into a huge one, but unfortunately the construction works only in theory. It involves constructing objects that, although we can describe them mathematically, are so complicated that they are impossible to make physically. You can read more about the Banach-Tarski theorem in the Plus article Measure for measure.

A statement which appears true, but may be self-contradictory in fact, and hence false. Type 2 paradoxes follow from a fallacious argument. Sliding puzzles and vanishing pictures are paradoxes of this type, as we shall point out later in this section. A statement which may lead to contradictory conclusions.

This is also known as an antinomy and is considered an extreme form of paradox, perhaps having no universally accepted resolution. Russell's paradox and one of its alternative versions known as the barber of Seville paradox is one such example.

In this paradox, there is a village in which the barber a man shaves every man who does not shave himself, but no one else. You are then asked to consider the question of who shaves the barber. A contradiction results no matter the answer, since if he does, then he shouldn't, and if he doesn't, then he should. You can find out more about this paradox in the Plus article Mathematical mysteries: Sliding Puzzles Sliding puzzles are examples of type 2 paradoxes.

These are fallacies which are often difficult to resolve. Let's consider a few of the more famous or infamous types of sliding puzzles. The first type of sliding puzzle we consider is the Nine bills become ten bills puzzle shown in figures 9 and In figure 9 nine twenty-pound notes are cut along the solid lines. The first note is cut into lengths of one-tenth and nine-tenths of the original note.

The second note is cut into lengths of two-tenths and eight-tenths of the original note. The third note is cut into lengths of three-tenths and seven-tenths of the original note.

Continue in this fashion until the ninth note is cut into lengths of nine-tenths and one-tenth of the length of the original note. In figure 10 the upper section of each note is slid over onto the top of the next note to the right. The result is ten twenty-pound notes, when originally there were only nine notes. Casual viewers may be tricked into thinking an additional note has been magically produced unless they measure the lengths of the ten new notes.

The deception is explained by the fact that each new note has length nine-tenths of the length of the original twenty-pound note.

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The more cuts used in such an incremental sliding puzzle, the more difficult it is to detect the deception. Apparently, someone actually attempted this trick in pre-war Austria. Another type of sliding puzzle appears to create a hole after sliding is completed. The paradoxical hole puzzle in figure 11 is an example. The square on the left of figure 11 is cut along the solid lines into three pieces, and then the pieces are rearranged as indicated, with the result that a hole appears in the square while the area apparently remains the same!

The deception is exposed in figure The paradoxcial hole explained. When you rearrange the pieces of the original square as shown in figure 11 a small difference becomes evident. The resulting square B is in fact a rectangle, as shown in figure Its vertical sides are a tiny bit longer than those of the original square A.

The difference in area equals the area of the hole.

Hence, no part of the original square A has disappeared, but the area of the hole is redistributed throughout the area of at the bottom of square B.