#Rhombus just-geometry-and-complexity

[lighthousenewsnetwork]

Move over, Pythagoras, because Ed Sheeran has just dropped a mathematical masterpiece disguised as a catchy pop tune. Yes, you read that right. Your latest shower song, "Shape of You," isn't just about a girl with a dance like a "Puerto Rican sunrise" (whatever that means, Ed?), it's a complex geometric puzzle waiting to be unraveled. Don't believe us? Let's break it down, shall we? Take the very first line: "I'm in love with the shape of you." This, my friends, is a blatant reference to the unit circle, that fundamental building block of trigonometry. Sheeran is clearly smitten by the perfect balance and harmony of a circle with a radius of one – a true geometer's dreamboat. And then there's the chorus: "The way you fit me like a glove." This, obviously, refers to the concept of a tangent line – a line that touches a curve at a single point, much like how Ed's heart (presumably shaped like a regular pentagon) perfectly connects with the object of his affection (a rhombus, perhaps?). But wait, there's more! Dr. Bartholomew Fitzwilliam, a renowned mathematician from the prestigious Institute for Pop Music Deciphering (IPMD), has dedicated his life to uncovering the hidden messages within chart-topping hits. After years of intense research (involving several thousand cups of cold brew and a questionable amount of gummy bears), Dr. Fitzwilliam has cracked the code. "The song's tempo," Dr. Fitzwilliam explains, eyes gleaming with mathematical fervor, "is a clear reference to the golden ratio, approximately 1.618. This, combined with the strategic use of major and minor chords, creates a sonic representation of the Fibonacci sequence!"     Hold on, Doc, before we all start picturing Ed Sheeran hunched over a dusty chalkboard scrawling complex equations, let's address the skeptics. "But Ed Sheeran isn't exactly known for his mathematical prowess," you scoff. To that, we say, pfft, details! Perhaps inspiration struck him after a particularly mind-numbing calculus lecture in high school, or maybe it was a late-night Wikipedia rabbit hole gone awry. Who knows? The point is, "Shape of You" transcends mere pop music. It's a gateway drug to the fascinating world of geometry! And if you think this is the only song hiding a mathematical secret, you're sorely mistaken. Take, for instance, Beyonce's "Crazy in Love." This is clearly a treatise on the Pythagorean Theorem, with lyrics like "I don't care, I'm just crazy in love" representing the disregard for logic when overcome by passion (a+b)^2 = c^2, baby! So, the next time you hear your favorite song, don't just tap your foot and sing along. Put on your thinking cap and unleash your inner Euclid. Who knows, maybe you'll discover that Taylor Swift's "Shake It Off" is actually a complex dissertation on the theory of relativity, or that "Baby Shark" is a terrifying prophecy about the impending black hole takeover. The possibilities are endless! Now, go forth and decode! Share your outrageous mathematical interpretations of popular songs with your friends and family. Remember, there's more to music than meets the ear – there could be a whole universe of geometry lurking beneath the catchy melodies. Just don't blame us if your next trip to the grocery store turns into a feverish debate about the parabolic arc of a banana.

[the-treeangle]

Have a table to hide *generously place down wooden table* - Rhombus just-geometry-and-complexity

“Nice hat.”7/15

[mathematicianadda]

Small Sets of Arc-Sided Tiles

Tim has previously written guest posts here about tiling by tricurves, and is now looking at ways of tiling with other shapes.

In an earlier post elsewhere I covered some basic arc-sided shapes that tile by themselves. Lately I’ve been playing with groups of curved tiling shapes, asking a question common for me: how to get the most play value as an open-ended puzzle? This means getting the most interesting possibilities from the simplest set. “Interesting” includes variety, complexity, challenge and aesthetic appeal. “Simplest” covers not only size of set and the shapes, but also the least total information needed to describe or construct the shapes.

My simple approach here is to start out with one interesting main shape and see what other (minor) shapes are needed to fill in the gaps, by trial and error; then try to refine and optimize that set to make it, in a sense, efficient.

For this post I’ve avoided the frameworks of the self-tiling regular triangles, squares and hexagons. Let’s look at two main shapes: the first is based on the pentagon; the second is a tricurve.

Using Pentagons

The regular pentagon of course can’t tile by itself. The set of tiles needed to help tile the plane with regular pentagons is well known. But let’s replace the sides of a regular pentagon with concave arcs of 72°.  We can lay these out in various ways to get different types of gaps, as shown here:

Note in many cases a point is hitting midpoint on a neighboring arc. Many of these gaps can be filled with simple lens shapes of 36°, 72° and 108°:

The remaining gaps need to be filled with partial lenses: 72° or 108° lens with one or more chunks gone. To fill the remaining gaps as is would require at least four more shapes. But we can reduce this number by backing up and combining the smaller tiles. If we start with the 36° lens and add a 4-side concave diamond (with corners of 36° and 144°, and 36° concave arcs) we can get the 72° lens and any partial 72° lens. In order to make the 108° lens we need to use another concave diamond, with corner angles of 72° and 108°.  This also lets us fill out the end of the elongated 108° lens shape.

So now the part count is four shapes (above): one major and three minor, and these let us fill the gaps:

If this were a real puzzle we would probably complain about the large number of little 36° lens pieces. Can we use less of these? The 36° lens only needs to be separate from the 4-concave diamonds in the cases where the lenses would overlap. We can permanently attach two of the 36° lenses to the thin diamond; and attach three 36° lenses to the wide diamond. So now our minor shapes look like this:

 and the tiling looks like this:

This set of tiles seems a reasonable solution (although other similar sets are possible). Now rather than simply filling gaps, we can start exploring various tilings:

Using Tricurves

The second main shape is a 36°-72°-108° tricurve, which is quite different. The tricurve already has great flexibility for tiling by itself periodically, non-periodically, and radially (as shown in previous post). So any additional parts should add to the possibilities – and it doesn’t take much. Even adding a single 36° or 72° lens at the center of a radial tiling opens many possibilities:

Since the underlying geometry is similar let’s start out with our original three minor shapes: the 36° lens and the two 4-sided concave diamonds. These let us create a very wide range of tilings:

Some of these patterns are of course not sustainable for tiling the plane. The additional complexity allowed comes partly from a means to fill gaps between adjoining convex sides or concave sides. Each of the three minor shapes by itself can add to tricurve tiling complexity, as can the use of any two of the minor shapes. Also the minor shapes can tile without the main shape –which the pentagon minor shapes can’t do (Why not?).  

Because of the ways a tricurve can tile with itself, there are many more opportunities for odd-shaped gaps that can’t be covered with the three minor shapes. With the tricurve the tiling is much more open-ended that with the pentagon above. There are no doubt various other minor shapes that could be added to fill gaps, but we’ll stick with these three for now. This whole set is interesting since it consists partly of nested lens shapes:

Also the tricurves—or either of the concave-diamond shapes for that matter—can make a circular hole, which can be filled with a circle made of the set or just the minor pieces:

Thoughts on tiling set design

Designing a small tiling set involves making tradeoffs between shape complexity, part count, and aesthetic appeal. In both shape sets, part of the complexity of the final tiling is in the use of the arcs. There is a pattern of arcs interwoven with the pattern of shapes; this may be seen as full or partial circles, or in the patterns of the arcs as they branch and connect. Also we can choose shapes to make tiling (as a puzzle) more challenging; for instance, if we modify the concave-sided pentagon so one of its sides is a convex arc, tiling will require more thought and thus be more interesting.

Both main shapes above are of course compatible with the minor shapes. This is not surprising since all the shapes incorporated 36 and 72 angles. The underlying diamonds with corners of 36° and 144°, or 72° and 108°, are two rhombus shapes used in a version of the Penrose tiles.

We could of course reduce these sets and their tilings by replacing all 36° arcs with straight lines (facets). The 36° lens shape disappears, reducing the set part count and the count of the lens pieces in the tiling.

Surprisingly, this reduction by faceting makes some things a little more complex. The larger arcs of the two main shapes would now be more complex to describe and construct. Since we sometimes connected at the midpoint of pentagon’s concave side, we’ll need to describe the shape as having ten faceted sides. Likewise, to keep the effect of the concavity of the smallest arc, the faceted equivalent of the tricurve needs 12 sides and four unique angles –whereas the much simpler tricurve can be described with two angles (36° and 72° – the 108° is the simple sum and redundant).

Compared to structurally equivalent tilings with faceted tile shapes, the above arc-sided sets:

have the additional part count of the 36° lens shape

have more complex diamond shapes, due to their 36° arcs

have main shapes that are simpler to describe and construct

have the aesthetic appeal and interest of connected arcs; and

overall provide more challenge and play value.

Further possible investigations:

What happens when we use both the concave pentagon and the tricurve as main shapes in the same set?

What other main shape would you try as a starting point?

from The Aperiodical https://ift.tt/2MNT7kT from Blogger https://ift.tt/2Ngj8bz

[hugecount]

How Can We Make Packaging Fascinating That Our Customers Love? | Hugecount

To buy a product firstly its appearance, color, size, and design are taken into consideration. In short, if you want to buy an item, their outlooks and the way they are presented to you provokes you towards it. So taking our clients as our priority, we have to think of how we can make packaging fascinating that our customers love. From the old times, things are being wrapped up in different ways so to make them attractive and appealing for the buyer.

Square rectangles or circle:

Let’s came out of the stereotype of custom boxes that we have and move to the new shapes of the geometry.  We have other shapes like oval, trapezium, rhombus, kite, and diamond shapes that can be used as 3d model containers. Whenever you think of buying a commodity, you surely look at the container in which it is presented to you. If it beautifies, it makes you happy, and you tend to buy more of that item, but if it is wrapped, insignificantly, the insider loses its worth too. The containers can be a box or a bag. But the shape of the case in which you are going to hold it must not alter the way of the belonging you just bought. And it should not be so congested that you have to squeeze it in. For example, a pizza which is a circle in shape is placed in a square box giving it enough space. But now you can use a circle-shaped box for it as well. And why not a triangular-shaped packaging for a piece of the pizza. Thus the size of the carrier tells us a lot about the product used or delivered to a person.

Simplicity should never fall apart:

Never choose complexity over the simplicity as it directly affects the rate of a person’s mind whether to buy a product or not. The simple and unique qualities of cardboard boxes seem more compelling to buy. The customer love to buy a simple and delicate nature of boxing. You can see the classy and elegant design of the Apple manufacturers. Their first and foremost motive is the ease of their clients. They have a single colored box with all the entities adjusted inside however on the outside showing the product name, logo and information about the item

Cool and be creative:

Sometimes you have to go with the new ideas so that it can make your product being sale hand in hand. The gathering of things should be done in such an exciting way. It should have a style and charms in it that make the consumer buy it for sure. It should arise a feeling of wanting, a sense of purchasing it whether he or she needs it or not. For example, the cosmetic accessories are mostly boxed up in transparent things making their vibrating colors provoking female aesthetic senses to buy that product. They choose natural colors so making the shelve look like a rainbow as all the colors are available in that range. So this way Carriers are a bonus to your sales. For example, you can make the fruit juices packs in the shape of their flavored fruit. It is easy and more informative for the patron to know which flavor he is drinking.

Be an icon:

Seems challenging, but it is happening! Why not make your enclosure so distinctive that a customer can identify it by its shape. The style of the encapsulating should speak for itself, just like the brand of Coca-Cola. For a century, they have the same trend of their glass bottle that anyone can identify by holding it in hand quickly. The shape and style say it all.

Your product can be your inspiration:

We need a box or bag when mostly we want to gift someone a present. So, in this case, your product should itself be an inspiration for its casing. Gift boxes are of many types they can be made of simple cardboard or exclusively made of glass. They can be of plastic or woody material. Nowadays, trends have changed so much that it is not necessary to conceal your product completely. For that reason, even the gifts are wrapped in a transparent sheet of paper or net. The transparency of the enclosure gives the mindful sight of the ravishing element inside. This makes the wrapping easy and light weighted too.

Source: https://hugecount.com/business/how-can-we-make-packaging-fascinating-that-our-customers-love/

[learningpundits]

Tips on Non-Verbal Reasoning Test Questions For Pattern Matching

5 TIPS on Cracking Aptitude Questions on Pattern Matching

Tip #1: Find the sequence of transformations applied on the figures

Some common transformations that are followed in this type of questions are:

Rotation: A part or whole of the figure may be rotated by a certain angle.

Illustration 1: Select a suitable figure from the answer figures to replace (?)

In the figures, the shaded leaf rotates by 225⁰ in the clockwise direction while the un-shaded leaf rotates by 225⁰ in the anti-clockwise direction. Scanning through the options, we see that the 3rd figure satisfies these conditions. Thus, the answer is 3.

Enclosure: A specific part or whole of the figure may be enclosed in some shape.

Sides/ Lines: The number of sides/ lines in the figure may follow a certain progression.

Illustration 2: Select a suitable figure from the answer figures to replace (?)

In these figures, the polygon rotates 90⁰ Clock-Wise, gets smaller in size and gets enclosed by a figure with one less side than itself. So the last figure will have a rhombus enclosed in a triangle. Thus, the correct answer is 1.

Vertical/ Lateral Inversion: The figure may be inverted vertically, laterally, or both during successive transformations.

Illustration 3: Select a suitable figure from the answer figures to replace (?)

Figure B is the result of vertical inversion of A. We may, thus, conclude that a figure is vertically inverted in the subsequent figure. Thus, the missing figure will be an inverted form of C. Looking at the answer figures, we see that figure 1 follows this transformation. Thus, the answer is 1.

Shifting: A specific or whole of the figure may be shifted in any direction.

Combination: A figure may follow more than one of the above mentioned transformations.

Illustration 4: Select a suitable figure from the answer figures to replace (?)

Except for the dots, the remaining part of the figure gets inverted and shifts to the opposite side of the square boundary. Thus, in the final figure, the sign ‘<‘will be inverted and will shift to the left side of the square boundary. This will be figure 3 from the answer figures. Thus, the answer will be 3.

Tip #2: Break the figure into smaller parts to identify the pattern for figure completion

Following are some of the ways of splitting a figure into smaller parts:

Geometry: The figure may be broken into circles, triangles, quadrilaterals, polygons, etc. that overlap, touch each other, enclose some shape(s), or are just parts of the figure.

Illustration 5: Identify the figure that completes the pattern.

Each quarter of the triangle consists of 2 right angled triangles. Thus, option D is correct.

Illustration 6: Identify the figure that completes the pattern.

The missing section should have 4 lines. One of these lines should touch the bottom left of the square and another should touch the top right. Only (D) matches these requirements.

Tip #3: Classify the figures on the basis of sides, geometry or dimensions

Some of the common classification bases are as follows:

No. of Sides: Figures can be classified depending on the no. of sides they have. Type of geometry: The figures may be classified as triangles, quadrilaterals, circles, etc. Dimension: You may classify the figures as 2-D or 3-D figures. Conjoined, enclosed, or overlapping: Some figures may be complex, consisting of conjoined shapes, smaller shapes enclosed within larger ones and/or partially or completely overlapping shapes, while others might be simple.

Illustration 7: Group the given figures into 3 classes using each figure only once.

The given figures can be classified on the basis of number of sides. Figures 1, 6 and 9 have 3 sides each; 3, 4 and 7 have 4 sides each; 2, 5 and 8 have 5 sides each.

Answer: 1, 6, 9| 3, 4, 7| 2, 5, 8.

Illustration 8: Group the given figures into 3 classes using each figure only once.

1, 2 and 7 are simple figures.

3, 5 and 9 each have one shape enclosing another smaller shape.

4, 6 and 8 each have two shapes each that are touching each other.

Thus, the given figures can be classified as:

1, 2, 7| 3, 5, 9| 4, 6, 8.

Tip #4: Analyze the options one by one and eliminate choices that do not follow the rule

Illustration 9: Choose the set of figures which follows the given rule.

Rule: Closed figures gradually become open and open figures gradually become closed.

The 1st choice can be eliminated since in the 2nd figure itself, the inner circle does not open, but is replaced by a triangle. In the next set, the inner square does not open in the 2nd figure. All the figures in the 3rd option follow the rule, with the rectangle opening up and the straight line inside it closing into a rhombus. Thus, the answer is (3).

Illustration 10: Choose the set of figures which follows the given rule.

Rule: As the circle decreases in size, its sectors increase in number.

In the 1st option, though the size of the circle decreases, the no. of sectors remains the same. In the 2nd option, the no. of sectors in the 4th figure is less than that in the 3rd. Again in the 3rd choice, the no. of sectors in the 2nd figure is less than that in the 3rd. Thus, none of these options follow the rule. The correct answer is (D) and we may confirm that in the 4th option, the size of the circle decreases consistently while the no. of sectors increases.

Tip #5: Complexity of a figure is determined by the no. of sides, shapes, sections, etc. When a figure is said to become simpler, it means that one or more of the following happens:

Lines: If the no. of consistent lines of the figure continuously decreases, then it may be concluded that the figure is becoming simpler. In other words, if the no. of sectors of the figure keeps decreasing, then it is said to be becoming simpler. Shapes: If a figure becomes simpler, the no. of shapes consisting some part or whole of the figure keeps on decreasing consistently. Curves: The figures may also consist of certain curves. The extent or length of the figure keeps decreasing as the figure becomes simpler. Opening of figure: At times, a part or whole of the figure opens up, thus making it simpler.

Illustration 11: Choose the set of figures which follows the given rule.

Rule: The series becomes simpler as it proceeds.

Analyzing the sets one by one, we see:

In the 1st set, the no. of sectors initially decreases, making the figure simpler, but then in the 5th figure, it again increases. Similarly, in the 2nd set, the complexity increases and decreases alternately. So none of them follow the rule. The figure in the 3rd choice, however, keeps becoming simpler as the no. of leaves and lines inside the circle keeps decreasing. The correct answer is (3).

Illustration 12: Choose the set of figures which follows the given rule.

Rule: The series becomes more complex as it proceeds.

Analyzing the sets one by one, we see:

In the 1st set, the last figure is simpler than its preceding one in that the curve forming the vein of the leaf shortens. Considering the 2nd set, the 4th figure is simpler than the 3rd one since the lower left circle opens up. So, both these options are eliminated. Now, the 3rd set keeps becoming complex as the no. of sectors, and then triangles (at the edges), keeps increasing. Answer: (3).

Illustration 13: Choose the set of figures which follows the given rule.

Rule: The series becomes more complex as it proceeds.

Again, we analyze the options one by one.

The 1st set can be eliminated as it alternates between becoming simpler and complex owing to the no. of lines in the figure. The 2nd option keeps becoming more complex as the no. of lines and hence, sectors, keeps increasing. Thus, the correct answer is (2).

(contd..) Tips on Non-Verbal Reasoning Test For Pattern Matching - https://learningpundits.com/module-view/85-pattern-recognition/1-tips-on-pattern-recognition/

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[miamibeachbroker]

Sweetbird

New Post has been published on http://www.mii.miami/sweetbird/

Sweetbird

Sweetbird

92 Northeast 40th StreetMiami

Architect Jeanne Gang, known for turning structures inside out with her unique exo-spatial high-rise design technique, is back on the block with recently unveiled designs for a stunning 14-story residential tower in Miami’s Design District. The tower, reportedly called Sweetbird South Residences, promises panoramic views of Biscayne Bay from each of the building’s proposed 76 units.

Units: 76 Stories: 14

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Sweetbird Condo Description

Architect Jeanne Gang, known for turning structures inside out with her unique exo-spatial high-rise design technique, is back on the block with recently unveiled designs for a stunning 14-story residential tower in Miami’s Design District. The tower, reportedly called Sweetbird South Residences, promises panoramic views of Biscayne Bay from each of the building’s proposed 76 units. Recently released renderings show Sweetbird South as a residential building anchored by two stories of ground floor retail space, a resident lounge and a rooftop swimming pool. The tower is obvious on form and subtle on function. The building appears to be rippling or trembling but definitely not falling. Each residence features floor-to-ceiling windows and oblique-angled terraces that form seemingly implausible quadrilateral shapes–trapezoids, parallelograms and rhombuses. Jeanne Gang must have aced geometry as a student. The Miami tower features ground floor retail space, a resident lounge, a rooftop swimming pool, floor-to-ceiling windows and shaped terraces. While most people can’t discern between a trapezoid and a rhombus, Studio Gang transforms buildings into intriguing geometrical experiments—as if the firm is attempting to solve complex mathematical theorems on the façade of skyscrapers. The Sweetbird South building is begging to be deciphered but perhaps only Euclid or our college math professor could break its code.

The tower’s interior extends outside to the façade, producing a dynamic spatial (or exo-spatial) arrangement of habitable spaces that function as a contemporary “Florida room.” According to the firm, “these shaded, open-air rooms provide both a thermal buffer for the interior and an outdoor space for relaxing and entertaining.” See, we told you—subtle on function (and there are even plans to integrate solar shade and rainwater collection into the design). What better location to bring indoors outside than in Miami overlooking Biscayne Bay?

The Sweetbird South tower feels like the southeast companion to Studio Gang’s 15-story design called City Hyde Park in Chicago.

There’s something distinctly Flat Iron about this Miami building (the way it dominates its short block in seemingly triangular fashion), except it’s bright white, modern and offers better views. Is it like an Antoni Gaudí structure in Barcelona? Not quite, but it’s absolutely a head scratcher and eyeball burner—in a good way. Studio Gang’s Miami tower is a residential building disguised as an optical illusion—or is that vice versa? Perhaps we can describe it better this way—it’s a rhetorical question mark that doesn’t need to answer to anyone. It is what it is.

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Peloro, Miami Beach 6620 Indian Creek Drive Miami Beach Life on the water has always been about exploration and discovery. On the bayside shores of Miami Beach, Peloro is about [...]

Alexander 2017-04-17T13:05:11-04:00

Hyde Beach House, 4000 South Ocean Drive, Hollywood, FL 33019

Hyde Beach House 4000 South Ocean Drive Hollywood Hyde House Hollywood is a new project located on Hollywood Beach, in the heart of South Florida. The building is perfectly situated [...]

Alexander 2017-04-17T12:49:08-04:00

Jade Signature, 16901 Collins Ave, Sunny Isles Beach, FL 33160

Jade Signature 16901 Collins Ave Sunny Isles Beach Jade Signature’s extraordinary resort-like experience is further enhanced by having three floors entirely dedicated to amenities and 53 stories of elegantly sculptural, [...]

Alexander 2017-04-17T19:54:25-04:00

Gran Paraiso, 600 NE 31st St, Miami, FL 33137

Gran Paraiso 600 NE 31st St Miami Gran Paraiso - a new project of the developer The Related Group, located in Miami at 600 Northeast 31st Street. The building has [...]

Alexander 2017-04-17T20:20:52-04:00

ECHO Brickell, 1451 Brickell Avenue, Brickell, FL 33131

ECHO Brickell 1451 Brickell Avenue Brickell ECHO Brickell is an exclusive high-rise boutique-style hotel in the heart of Miami that will be constructed on the east side of Brickell Avenue. [...]

Alexander 2017-08-13T01:15:50-04:00

Brickell Heights, 850 South Miami Avenue, Brickell, FL 33130

Brickell Heights 850 South Miami Avenue Brickell Scheduled to be completed in 2017, Brickell Heights is one of the newest and most anticipated real estate developments in Brickell area. A [...]

Alexander 2017-04-19T14:26:50-04:00

Biscayne Beach Miami, 711 Northeast 29th Street, Miami, FL 33137

Biscayne Beach Miami 711 Northeast 29th St Miami Biscayne Beach is luxury condominium, being developed in cooperation of Eastview Development and GTIS Partners in Miami’s East Edgewater neighborhood. World-known [...]

Alexander 2017-04-19T15:41:09-04:00

Auberge Residences & Spa, 1440 South Biscayne Boulevard, Miami, FL 33132

Auberge Residences & Spa 1440 Biscayne Boulevard Miami Auberge Residences & Spa - a new residential 60-storey skyscraper, which will be located at 1440 South Biscayne Boulevard, Miami. The project [...]

Alexander 2017-04-19T15:44:15-04:00

Auberge Beach Residences & Spa, 2200 North Ocean Boulevard, Fort Lauderdale, FL 33305

Auberge Beach Residences 2200 North Ocean Boulevard Fort Lauderdale Each Auberge property is unique and authentic to its location. Carefully curated activities highlight the most desirable aspects of the surrounding [...]

Alexander 2017-04-19T15:48:27-04:00

Armani House, 18975 Collins Ave, Sunny Isles Beach, FL 33160

Armani House, Sunny Isles 18975 Collins Ave Sunny Isles Beach Armani House by Cesar Pelli is a new oceanfront master-peace, located in a luxury high-rise condominium community, Sunny Isles Beach.Armani [...]

Alexander 2017-04-19T15:53:26-04:00

Aria on the Bay, 1770 N Bayshore Dr, Miami, FL 33132

Aria on the Bay 1770 N Bayshore Dr Miami Aria on the Bay is a new luxury residential high-rise development by Architectonica, an internationally renowned architectural firm. Aria on the [...]

Alexander 2017-04-19T15:56:57-04:00

AquaBlu, 920 Intracoastal Drive, Fort Lauderdale, FL 33304

AquaBlu Fort Lauderdale 920 Intracoastal Drive Fort Lauderdale AquaBlu - a new residential building located in Fort Lauderdale at 920 Intracoastal Drive near the historical monument Bonnet House Museum and [...]

Alexander 2017-04-19T15:00:45-04:00

AVVA Residences

AVVA RESIDENCES, AVENTURA  Country Club Drive & 34th Street Aventura A sumptuous residential complex Avva Residences is one of the best luxury buildings located in the center of Aventura, just in [...]

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Move over, Pythagoras, because Ed Sheeran has just dropped a mathematical masterpiece disguised as a catchy pop tune. Yes, you read that right. Your latest shower song, "Shape of You," isn't just about a girl with a dance like a "Puerto Rican sunrise" (whatever that means, Ed?), it's a complex geometric puzzle waiting to be unraveled. Don't believe us? Let's break it down, shall we? Take the very first line: "I'm in love with the shape of you." This, my friends, is a blatant reference to the unit circle, that fundamental building block of trigonometry. Sheeran is clearly smitten by the perfect balance and harmony of a circle with a radius of one – a true geometer's dreamboat. And then there's the chorus: "The way you fit me like a glove." This, obviously, refers to the concept of a tangent line – a line that touches a curve at a single point, much like how Ed's heart (presumably shaped like a regular pentagon) perfectly connects with the object of his affection (a rhombus, perhaps?). But wait, there's more! Dr. Bartholomew Fitzwilliam, a renowned mathematician from the prestigious Institute for Pop Music Deciphering (IPMD), has dedicated his life to uncovering the hidden messages within chart-topping hits. After years of intense research (involving several thousand cups of cold brew and a questionable amount of gummy bears), Dr. Fitzwilliam has cracked the code. "The song's tempo," Dr. Fitzwilliam explains, eyes gleaming with mathematical fervor, "is a clear reference to the golden ratio, approximately 1.618. This, combined with the strategic use of major and minor chords, creates a sonic representation of the Fibonacci sequence!"     Hold on, Doc, before we all start picturing Ed Sheeran hunched over a dusty chalkboard scrawling complex equations, let's address the skeptics. "But Ed Sheeran isn't exactly known for his mathematical prowess," you scoff. To that, we say, pfft, details! Perhaps inspiration struck him after a particularly mind-numbing calculus lecture in high school, or maybe it was a late-night Wikipedia rabbit hole gone awry. Who knows? The point is, "Shape of You" transcends mere pop music. It's a gateway drug to the fascinating world of geometry! And if you think this is the only song hiding a mathematical secret, you're sorely mistaken. Take, for instance, Beyonce's "Crazy in Love." This is clearly a treatise on the Pythagorean Theorem, with lyrics like "I don't care, I'm just crazy in love" representing the disregard for logic when overcome by passion (a+b)^2 = c^2, baby! So, the next time you hear your favorite song, don't just tap your foot and sing along. Put on your thinking cap and unleash your inner Euclid. Who knows, maybe you'll discover that Taylor Swift's "Shake It Off" is actually a complex dissertation on the theory of relativity, or that "Baby Shark" is a terrifying prophecy about the impending black hole takeover. The possibilities are endless! Now, go forth and decode! Share your outrageous mathematical interpretations of popular songs with your friends and family. Remember, there's more to music than meets the ear – there could be a whole universe of geometry lurking beneath the catchy melodies. Just don't blame us if your next trip to the grocery store turns into a feverish debate about the parabolic arc of a banana. #EdSheeran #Geometry #Music #Satire #ShapeofYou