Fun Fact Friday: When Beetles Go Rogue

To celebrate the recent publication of Beetles of Eastern North America, Arthur V. Evans’s tremendously beautiful and comprehensive guide to all creatures coleopteral, we’ll be posting a new “fun fact” about beetles each week. These anecdotes won’t be limited to your standard beetle biology; they’ll surprise you, make you laugh, and wish that you’d bought the book sooner!

Did you know? 

7-24 BeetleIn this week’s edition, we’re bringing you a story all the way from Los Angeles’s Griffith Park. In a rare twist of irony, it seems that the pine tree planted to honor the memory of former Beatles lead guitarist George Harrison has been overrun and subsequently destroyed by beetles of the family Curculionidae.

7-24 HarrisonTree

While the specific type of bark beetle that bested the tree isn’t included in the Eastern edition, we won’t have to wait very long to solve this entomological enigma; Arthur V. Evans is already hard at work on part two, aptly titled Beetles of Western North America

So, now you know: if you’re looking for a self-sustaining weed-wacker, look no further than the beetles in your backyard!

Photo credit: Breakingnews.ie

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Arthur V. Evans is the author of:

7-24 Beetles2 Beetles of Eastern North America
Paperback | 2014 | $35.00 / £24.95 | ISBN: 9780691133041
560 pp. | 8 x 10 | 1,500+ color illus. 31 line illus. | eBook | ISBN: 9781400851829 | Reviews  Table of Contents  Preface[PDF]  Sample Entry[PDF]

The Imitation Game — Official Trailer (Release date: November 21, 2014)

The Imitation Game is based on Alan Turing: The Enigma. We will release a movie tie-in paperback later this year so look for details of this soon.

A Look at De-Extinction on TED Radio Hour

What if you could bring an extinct animal back to life? This week on the TED Radio Hour, Guy Raz interviews Stewart Brand, an environmentalist and founder of The WELL and the Global Business Network. Brand says that we now have technology that is advanced enough to bring back extinct creatures like the passenger pigeon, a bird that became extinct when the last member, Martha, died in the Cincinnati Zoo. This year marks the centennial anniversary of Martha’s death and the extinction of her species.

This NPR segment, entitled “The Hackers” takes us to visit Martha in her resting place at the Smithsonian Institute. Brand discusses how DNA taken from Martha’s remains can be inserted into the DNA sequence of a related species, the band-tailed pigeon. More from Brand in his TED Talk below.

Check out Brand’s section of this week’s TED Radio Hour as well as the full broadcast.

Curious to know more about Martha? PUP author Errol Fuller discusses the extinction of her species in his new book, THE PASSENGER PIGEON. This stunningly illustrated book also tells the astonishing story of North America’s passenger pigeon, a bird species that–like the Mammoth and the Dodo–has become one of the great icons of extinction.

For a look at another extinct species that Brand mentions, the tylacine, take a look at photos from LOST ANIMALS, another book by Errol Fuller. The New York Times ran a photo slideshow here of rare photos of extinct animals.

thylacine 2

Birding in the Unknown: Tips and Tales from Birds of Peru Author Tom Schulenberg

[Note: Those of you who regularly read Princeton University Press's blog will have noticed that we have only featured posts by our colleagues and/or authors, however, when someone has the opportunity to travel to Peru, to meet with Tom Schulenberg (the lead author of Birds of Peru), and to see and talk about the birds of Peru at great length--you take them up on the offer of a guest post. We are pleased to present this guest article from Hugh Powell, a science editor at the Cornell Lab of Ornithology. We welcome your feedback on this type of article -- should we do more of this?]


 

tom_dennis-powell

Tom Schulenberg, center, and Dennis Osorio, left, search for an elusive subspecies of Rufous Antpitta in the Cajamarca highlands, Peru. Photo by Hugh Powell.

It’s not often a bird watcher gets the chance to tour a new country accompanied not just by a good field guide but by the field guide’s author. That’s what happened to me in May 2014, when I joined Tom Schulenberg on the World Birding Rally in northern Peru. Schulenberg, a research associate at the Cornell Lab of Ornithology, is the lead author of Birds of Peru.

Schulenberg_BirdsPeruSchulenberg describes his role in the book as almost accidental—he began visiting Peru in the late 1970s as a graduate student, and his original role with the book was just to help with maps. The true architects of the book, Schulenberg says, were John O’Neill (“the person who more than anyone else in the modern era put Peru on the ornithological map,” according to Schulenberg), and Ted Parker, the now-legendary field ornithologist whose career was cut tragically short in a plane crash in Ecuador in 1993. In the mid-1990s, Schulenberg took up the mantle of the book, recruiting ornithologists Doug Stotz (Field Museum of Natural History) and Dan Lane (Louisiana State University) as additional coauthors.

The field guide was a major undertaking—Peru is home to 1,800 species of birds, more than any country in the world except Colombia. The book was eventually published in 2007, nearly 35 years after O’Neill and Parker first envisioned it.

In late May, at the close of the 8-day rally (during which our group found nearly 800 bird species), I sat down with Schulenberg to learn more about the genesis of the book and the joys of birding in Peru—or, as he put it, “the fun of being completely overwhelmed by what you see.”

Why Peru? Was it just happenstance that you went there instead of somewhere else in the world?

tom_playback_ruiz
Tom Schulenberg plays the song of a unique subspecies of Rufous Antpitta using his phone. Photo by Flor Ruiz.

It wasn’t happenstance. I joined the AOU when I was in my early teens, and one of the first issues [of the Auk] I received was the issue in which John O’Neill and George Lowery described the Elusive Antpitta from this indigenous village called Balta near the Brazilian border. There was this color frontispiece of an antpitta, and the introduction of the paper talks about how even after years of work, within a few square miles you can still be encountering species you didn’t know were in the area, and sometimes they might even be new to science. I was just totally blown away. I had no idea that people were still discovering new species of birds, and I was completely entranced by this idea of an avifauna so complex that you could be there for years and still be learning new things about it.

So you went to graduate school at Louisiana State University with O’Neill as your mentor. And pretty soon his prediction about finding new birds actually came true for you?

peru_powell-2
Cloud forest beneath a blanket of cloud at Alto Mayo, San Martin, Peru. Photo by Hugh Powell.

It’s not like I went to Peru really expecting to find new species—I was just trying to work on my life list. But the possibility always was there. And on my [second] trip to Peru we found several species that were undescribed or recently described. We found Cinnamon Screech-Owl, Megascops petersoni [like many tropical ornithologists, Schulenberg reflexively refers to birds by their scientific names in conversation]; Hemitriccus cinnamomeipectus, the Cinnamon-breasted Tody-Tyrant; Johnson’s Tody-Flycatcher, Poecilotriccus luluae; which actually had been collected in the 1960s by Ned Johnson from Berkeley, but at that time Ned had not yet gotten around to describing it. Grallaricula ochraceifrons, Ochre-fronted Antpitta, we caught two in a single night in adjacent nets. [But all those were in the process of being described by other scientists, and] “all” we got out of it was the Pale-billed Antpitta. It was a fantastic trip though—I’m not complaining.

What field guide did you use before Birds of Peru?

Now remember that when some of the greats first started going down, people like John Terborgh and John O’Neill, there was literally nothing except the primary literature. But in 1970 an ornithologist [named] Meyer de Schauensee published a one-volume guide to the birds of South America, and it had some illustrations, but the illustrations were not great, and there was basically no attempt to illustrate every species. Instead what you had was about a paragraph on each species.

chestnut-eared_aracari-perrins
Chestnut-eared Aracari at Lago Lindo, Peru. Photo by Niall Perrins.

It definitely was difficult to use, and we disparagingly and no doubt unfairly started referring to it as “Meyer de Schloppensee.” But you know, that was our bible from ‘77 until 1986 when Hilty and Brown published the really revolutionary Colombia field guide.

Why did you publish the book with Princeton?

In 1986 Princeton published the Colombia guide by Hilty and Brown, and it was just a total bombshell all across northern South America—it was very good. It was the size of a Manhattan telephone directory. Some birders would even buy copies and rip out the plates, which now that the book is out of print and copies sell for hundreds of dollars, you could cry over that. Anyway the Colombia book was one of the things that made us very comfortable with working with Princeton, because it was so good and set a very high bar.

The modern format of Birds of Peru—text facing illustrations on every page—left little room for text about each species. How did you handle that?

The shorter species accounts were a challenge in many ways. We had only 110 words per species, on average, so there’s no character development that’s for sure. We had to leave out a lot of words.

tom_tomas-powell
Tom Schulenberg, right, and Thomas Valqui, are experts on Peruvian birds and served as judges during the 2014 World Birding Rally. Photo by Hugh Powell

Because the illustrations were opposite the text, we rarely describe what the bird looks like, and that saves a lot of space. Instead we focused on things like aspects of its behavior, or its habitat associations, its vocalizations. We tried to point out what you really need to focus on to ID the species. And we got that information from a lot of very knowledgeable people. If you look in the book, I think we have the longest acknowledgments section on record.

Where are the best places to go birding in Peru?

Well the nice thing about watching birds is you can never be bored, and that’s certainly true in Peru. Wherever you end up, you’ll be seeing interesting species about which not much is known. Certainly there are some places that get a lot of attention. The altiplano, though it might not have the most species, has very remarkable things like the Diademed Sandpiper-Plover. And then down in the Amazonian lowlands, those are the most species-rich places, and it’s both challenging and very rewarding to bird there. There’s the dry deciduous forest in the northwest, where we were [during the World Birding Rally], it’s got lower diversity but incredibly high numbers of individuals. I’m always amazed to go into those forests and see the sheer number of birds that are in that habitat. And there are the foothills, the places where the Andean habitats mix with Amazonia, and there are lots of species occurring in these narrow elevational bands. Pretty much anywhere you are in Peru, there’s lots there.

What do you look forward to when you go birding in Peru?

coquette-fernandez
Rufous-crested Coquette near Moyobamba, Peru. Photo by Alfredo Fernandez.

Part of the fun of going down there is the experience of being overwhelmed by what you see. Especially in humid forest on the eastern slope, where you start to get the Amazonian influence. You’ll run into a tanager flock, and just the sight of all these birds running around in the treetops, it’s challenging and exciting at the same time.

But if you pay attention to that flock, and if you can get beyond the gaudiness of the Saffron-crowned Tanagers and the Golden Tanagers, there are all these other dull-colored birds. Don’t pass them over too quickly. There’s this whole other set of birds that, as you gain experience, you may find are more interesting. You know, What’s this foliage-gleaner? What’s this antwren? And you’ll start to get sucked into the whole depth of birds Peru has to offer.

People go gaga over Paradise Tanagers, but I’m more likely to get excited by something like a Gray-mantled Wren. That’s a bird that’s at relatively low density, it has a narrow elevational range, so you have to pay attention. But when you see it, it’s sort of a sign that I’m in a really nice spot here, and there are probably other things here that are worth looking for.

Do you have any practical tips for people traveling to Peru?

Well, first is, you should do it.

peru_powell-1
Looking down the valley of the Utcubamba River near Chachapoyas, Peru. Photo by Hugh Powell.

Then, let’s see: Study your field guide. Look at the range maps. There’s information in those maps, so don’t ignore it. Use eBird—it has become a great supplement to anyone traveling in Peru to find out what’s been seen where. Keep your binoculars clean, and have a great time.

Is there a best season?

Peru is so large and so variable, you can’t go wrong. It’s a little more rainy during our northern winter, especially in the southeast of the country, in Amazonia. You can get into more trouble there with roads that time of year. But it doesn’t really matter what season you go.

And how long a trip should a bird watcher plan to take?

I think something like three years is a good time frame to shoot for.

For the record, he was laughing. But at the same time, he also seemed perfectly serious.


Hugh Powell is a science editor at the Cornell Lab of Ornithology.


Read more about the World Birding Rally on the Cornell Lab blog, the ABA blog, Nature Travel Network, and 10,000 Birds.

Cue up The Bangles and join us as we Count Like an Egyptian with Fox News


Interested in learning more about how to do math like an ancient Egyptian, check out David Reimer’s book Count Like an Egyptian.

Call for Information: The Atlas of Migratory Connectivity for Birds of North America

We hope to publish the The Atlas of Migratory Connectivity for Birds of North America in 2016. The editorial team is asking for help in collecting data:

WOTH_ex1-231x300This book (and eventually the web based information) will fill an enormous knowledge gap about migratory connectivity as it is a mapping project that capitalizes largely on the historic band-recovery data from the USGS – Bird Banding Laboratory. After the recovery of literally millions and millions of bands, there has yet to be a comprehensive analysis and compilation of these data. The stories emerging for each species are spectacular, the connections between geographic places stunning, and the biological information priceless.

We want this atlas to be the most comprehensive source of information about migratory connectivity available. To make this possible, we will include all sources of connectivity information into each species’ map including sight recoveries of marked birds, stable isotope studies, geolocator, satellite and GSM telemetry work. Therefore we are reaching out to the ornithological community to request that you send us all information relating to migratory connectivity you might have or be aware of – published or unpublished on any species. Single data points are fine – we don’t want to miss anything! We will be collecting contributions through the end of 2014. All contributions included in the atlas will be properly acknowledged.

Please contact Amy Scarpignato with questions or to send your information. Thank you for considering this request and we look forward to hearing from you.

Peter P. Marra & Susan Haig

 

Reposted from http://www.migratoryconnectivityproject.org/atlas-of-migratory-connectivity-seeks-movement-data/

Be the first to read Zombies and Calculus — win an advance reading copy via Goodreads

Goodreads Book Giveaway

Zombies and Calculus by Colin Adams

Zombies and Calculus

by Colin Adams

Giveaway ends August 10, 2014.

See the giveaway details
at Goodreads.

Enter to win

Celebrate the Red, White, and Blue… birds

We’re looking forward to the extended 4th of July weekend. To celebrate, we present our own version of red, white, and blue:

Untitled

These images are from The Crossley ID Guide: Eastern Birds. Learn more here: http://press.princeton.edu/titles/9384.html

van Grouw’s Anatomy: The Unfeathered Bird in Scientific American

Who knew anatomy could be ‘sexy?’7-2 van Grouw

So says paleozoologist and science writer Darren Naish in describing the natural science world’s renewed interest in the field. But it’s not because Katrina van Grouw gives a ‘stripped-down’ look at avian remains; rather, it comes courtesy of stream-lined CT scanning and sophisticated 3D visualizations. Yet, Naish’s praise of Katrina van Grouw’s artful spin on ornithology in this behind-the-scenes look at her life and work is much more nuanced than all that fancy stuff. His article in Scientific American explores the all-encompassing passion of this world-class ornithologist, meanwhile loudly complimenting her new book for its precision in rendering every minute muscle, bone, and tendon of the creatures that fill its pages.

Naish doesn’t just jot down his observations from the sitting-room chair; he is given the walking tour, complete with a perusal into the eccentric couple’s inner- and out-sanctums. For example: Katrina and Hein van Grouw are proud owners of a muntjac deer skull collection, a business of ferrets (live ones, it must be noted), and an unsurprisingly vast treasury of mounted bird skeletons, all of which Naish ogles with palpable envy. In many ways, the home epitomizes the research executed for and presented in The Unfeathered Bird: brimming with ornithological insight and too full of artifacts to dismiss as mere decorative ploy.


“It is simply imperative that you get hold of this book if you consider yourself interested in bird anatomy and diversity, or in anatomy or evolution in general.”


Despite van Grouw’s untimely release from her position at a natural history museum, which resulted from her desire to produce the book, Naish commends her for transforming the inconvenience into a wonderful opportunity and looks longingly into the future toward her forthcoming book on domesticates.

The ethically sourced remains of dogs, cats, chickens and pigeons make the cut for the tour, but together, they’re just a small fraction of the never-ending plethora of both bizarre and mundane critters that comprise van Grouw’s professional interests; and we, like Naish, hope to see them all expressed thus in due time.

Katrina van Grouw is the author of:

7-2 Unfeathered The Unfeathered Bird by Katrina van Grouw
Hardcover | 2013 | $49.95 / £34.95 | ISBN: 9780691151342
304 pp. | 10 x 12 | 385 duotones/color illus. | eBook | ISBN: 9781400844890 | Reviews Table of Contents Introduction[PDF]

Watch This: Digiscoping with Clay and Sharon, Episode 8 (Announcing the Winner!)

Sharon StitelerToday’s the day! In this final episode filled with thank-yous and shared memories, Sharon Stiteler of Birdchick reveals the theme of the series: good ol’ ROY G BIV (the rainbow). There were hints in Clay’s shirts and Sharon’s nail polish, and in the order of the birds themselves. Were you able to guess it?

And now: we know you’ve all been anxiously awaiting the announcement for the Winner of the Swarovski Spotting Scope, so without further delay: Congratulations to Peter Lawrence of Ottawa, Canada! Enjoy your new scope, brought to you by Swarovski Optik North America, Birdspotters Birding App, and of course, Princeton University Press.

Check out the episode here, and remember: when in doubt, visit south Texas!

Wildflower Wednesday: A Look at Summer’s Blossoming Bounty with Carol Gracie

Carol Gracie, queen of  flora, is at it again. Carol Gracie

The author of Spring Wildflowers of the Northeast: A Natural History has a new project in the works. The forthcoming book, to be called Summer Wildflowers of the Northeast, isn’t technically a field guide; but we’re betting it will be no less comprehensive. In it, Gracie plans to give a full account of the fascinating history of summer wildflowers: what pollinates them, what eats them, how their seeds are dispersed, as well as their practical and historical uses. The facts are further complemented by Gracie’s striking photographs, which we’ve sampled below. Be on the lookout for this one!

Carol Gracie is an acclaimed naturalist, photographer, and writer. Now retired, she worked for many years as an educator and tour leader with the New York Botanical Garden before teaming up with her husband, Scott Mori, on botanical research projects in South America. Her books include Wildflowers in the Field and Forest.

Enjoy these beautiful photos, and let us know in the Comments section which flowers you’ve noticed so far this season.

Monotropa Uniflora (Indian Pipe)
Opuntia humifusa showing ovaries
Datura stramonium
Nelumbo lutea
Platanthera ciliaris
Oenothera biennis
Lobelia cardinalis
Parnassia glauca
Solidago speciosa
Sarracenia purpurea

Monotropa uniflora (Indian Pipe)

Indian pipe is a flowering plant that lacks chlorophyll, the green pigment that allows plants to capture the sun's energy and allow them to produce carbohydrates. Instead, Indian pipe has a relationship with a fungus that absorbs nutrients from the roots of nearby trees and transports them to the underground parts of Indian pipe.

Opuntia humifusa (Prickly pear cactus) showing ovaries

Many people are surprised to learn that we have native cactus plants in the Northeast. Yet this species and a few others are adapted to surviving our cold northern winters. The lovely yellow flowers are pollinated by several species of bees.

Datura stramonium (Jimsonweed)

Farmers consider jimsonweed to be a noxious field weed, yet it produces lovely, fragrant flowers that don't open until almost sunset. The flowers are visited, and pollinated, by moths during the night. Jimsonweed played an important role in the colonial history of Jamestown, VA.

Nelumbo lutea (American lotus)

Our native lotus is a showy aquatic plant with large, orbicular leaves and the largest native flower in the Northeast. Many parts of the plant are edible.

Platanthera ciliaris (Orange fringed orchid)

Fringed orchids are pollinated primarily by butterflies, such as this spicebush swallowtail. Other species have flowers in shades of purple, white, or greenish-white.

Oenothera biennis (Evening primrose)

As its name suggests, evening primrose has flowers that open in the evening to attract their moth pollinators. One of the pollinators, the primrose moth (Schinia florida) also feeds on the plant as a larva, and may sometimes be found resting, partially camouflaged, in the flowers during daylight hours.

Lobelia cardinalis (Cardinal flower)

The deep, brilliant red of this flower is a beautiful, but sad, reminder that summer will soon draw to a close. Found in moist areas, cardinal flower provides a nectar source for hummingbirds that are migrating south in late summer.

Parnassia glauca (Grass-of-Parnassus)

Another late bloomer, grass-of-Parnassus has strikingly patterned flowers with bold green lines on a white background. Surrounding the true stamens is a ring of false stamens, each topped by a glistening yellow or green sphere that attracts insects. Grass-of-Parnassus is found in marshy seeps on limestone soils.

Solidago speciosa (Showy goldenrod)

Showy goldenrod is one of the latest species of goldenrod to bloom, filling meadows with its bright yellow flowers. Goldenrod meadows are a wonderful place to see the many species of insects that feed on, or get nectar from, goldenrod.

Sarracenia purpurea (Purple pitcher plant)

Pitcher plants live in nutrient-poor wetlands (acidic bogs or calcium-rich fens) and must supplement their nutritional needs with insects that are captured in their tubular leaves. Certain insects have evolved to withstand the digestive enzymes secreted by the leaf and use the pitcher plant as their only domicile.

Monotropa Uniflora (Indian Pipe)  thumbnail
Opuntia humifusa showing ovaries  thumbnail
Datura stramonium  thumbnail
Nelumbo lutea thumbnail
Platanthera ciliaris thumbnail
Oenothera biennis thumbnail
Lobelia cardinalis thumbnail
Parnassia glauca thumbnail
Solidago speciosa thumbnail
Sarracenia purpurea thumbnail

Concepts in Color: Beautiful Geometry by Eli Maor and Eugen Jost

If you’ve ever thought that mathematics and art don’t mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each.

With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important and beautiful branches of mathematics.

We’ve created this slideshow so that you can sample some of the beautiful images in this book, so please enjoy!

Plate 00
Plate 4
Plate 6
Plate 7
Plate 10
Plate 15.1
Plate 16
Plate 17
Plate 18
Plate 19
Plate 20
Plate 21
Plate 22
Plate 23
Plate 24.2
Plate 26.2
Plate 29.1
Plate 29.2
Plate 30
Plate 33
Plate 34.1
Plate 36
Plate 37
Plate 38
Plate 39
Plate 40.2
Plate 44
Plate 45
Plate 47
Plate 48
Plate 49
Plate 50
Plate 51

Beautiful Geometry by Eli Maior and Eugen Jost

"My artistic life revolves around patterns, numbers, and forms. I love to play with them, interpret them, and metamorphose them in endless variations." --Eugen Jost

Figurative Numbers

Plate 4, Figurative Numbers, is a playful meditation on ways of arranging 49 dots in different patterns of color and shape. Some of these arrangements hint at the number relations we mentioned previously, while others are artistic expressions of what a keen eye can discover in an assembly of dots. Note, in particular, the second panel in the top row: it illustrates the fact that the sum of eight identical triangular numbers, plus 1, is always a perfect square.

Pythagorean Metamorphosis

Pythagorean Metamorphosis shows a series of right triangles (in white) whose proportions change from one frame to the next, starting with the extreme case where one side has zero length and then going through several phases until the other side diminishes to zero.

The (3, 4, 5) Triangle and its Four Circles

The (3, 4, 5) Triangle and its Four Circles shows the (3, 4, 5) triangle (in red) with its incircle and three excircles (in blue), for which r = (3+4-5)/2 = 1, r = (5+3-4)/2 = 2, rb = (5+4-3)/2 = 3, and rc = (5+4+3)/2 = 6.

Mean Constructions

Mean Constructions (no pun intended!), is a color-coded guide showing how to construct all three means from two line segments of given lengths (shown in red and blue). The arithmetic, geometric, and harmonic means are colored in green, yellow, and purple, respectively, while all auxiliary elements are in white.

Prime and Prime Again

Plate 15.1, Prime and Prime Again, shows a curious number sequence: start with the top eight-digit number and keep peeling off the last digits one by one, until only 7 is left. For no apparent reason, each number in this sequence is a prime.

0.999... = 1

Celtic Motif 1

Our illustration (Plate 17) shows an intriguing lace pattern winding its way around 11 dots arranged in three rows; it is based on an old Celtic motif.

Seven Circles a Flower Maketh

Parquet

Plate 19, Parquet, seems at first to show a stack of identical cubes, arranged so that each layer is offset with respect to the one below it, forming the illusion of an infinite, three-dimensional staircase structure. But if you look carefully at the cubes, you will notice that each corner is the center of a regular hexagon.

Girasole

Plate 20, Girasole, shows a series of squares, each of which, when adjoined to its predecessor, forms a rectangle. Starting with a black square of unit length, adjoin to it its white twin, and you get a 2x1 rectangle. Adjoin to it the green square, and you get a 3x2 rectangle. Continuing in this manner, you get rectangles whose dimensions are exactly the Fibonacci numbers. The word Girasole ("turning to the sun" in Italian) refers to the presence of these numbers in the spiral arrangement of the seeds of a sunflower - a truly remarkable example of mathematics at work in nature.

The Golden Ratio

Plate 21 showcases a sample of the many occurrences of the golden ratio in art and nature.

Pentagons and Pentagrams

Homage to Carl Friedrich Gauss

Gauss's achievement is immortalized in his German hometown of Brunswick, where a large statue of him is decorated with an ornamental 17-pointed star (Plate 23 is an artistic rendition of the actual star on the pedestal, which has deteriorated over the years); reportedly the mason in charge of the job thought that a 17-sided polygon would look too much like a circle, so he opted for the star instead.

Celtic Motif 2

Plate 24.2 shows a laced pattern of 50 dots, based on an ancient Celtic motif. Note that the entire array can be crisscrossed with a single interlacing thread; compare this with the similar pattern of 11 dots (Plate 17), where two separate threads were necessary to cover the entire array. As we said before, every number has its own personality.

Metamorphosis of a Circle

Plate 26.2, Metamorphosis of a Circle, shows four large panels. The panel on the upper left contains nine smaller frames, each with a square (in blue) and a circular disk (in red) centered on it. As the squares decrease in size, the circles expand, yet the sum of their areas remains constant. In the central frame, the square and circle have the same area, thus offering a computer-generated "solution" to the quadrature problem. In the panel on the lower right, the squares and circles reverse their roles, but the sum of their areas ins till constant. The entire sequence is thus a metamorphosis from square to circle and back.

Reflecting Parabola

Ellipses and Hyperbolas

When you throw two stones into a pond, each will create a disturbance that propagates outward from the point of impact in concentric circles. The two systems of circular waves eventually cross each other and form a pattern of ripples, alternating between crests and troughs. Because this interference pattern depends on the phase difference between the two oncoming waves, the ripples invariably form a system of confocal ellipses and hyperbolas, all sharing the same two foci. In this system, no two ellipses ever cross one another, nor do two hyperbolas, but every ellipse crosses every hyperbola at right angles. The two families form an orthogonal system of curves, as we see in plate 29.2.

3/3=4/4

Euler's e

Plate 33, Euler's e, gives the first 203 decimal places of this famous number - accurate enough for most practical applications, but still short of the exact value, which would require an infinite string of nonrepeating digits. In the margins there are several allusions to events that played a role in the history of e and the person most associated with it, Leonhard Euler: an owl ("Eule" in German); the Episcopal crosier on the flag of Euler's birthplace, the city of Basel; the latitude and longitude of Königsberg (now Kaliningrad in Russia), whose seven bridges inspired Euler to solve a famous problem that marked the birth of graph theory; and an assortment of formulas associated with e

Spira Mirabilis

Epicycloids

Plate 36 shows a five-looped epicycloid (in blue) and a prolate epicycloid (in red) similar to Ptolemy's planetary epicycles. In fact, this latter curve closely resembles the path of Venus against the backdrop of the fixed stars, as seen from Earth. This is due to an 8-year cycle during which Earth, Venus, and the Sun will be aligned almost perfectly five times. Surprisingly, 8 Earth years also coincide with 13 Venusian years, locking the two planets in an 8:13 celestial resonance and giving Fibonacci aficionados one more reason to celebrate!

Nine Points and Ten Lines

Our illustration Nine Points and Ten Lines (plate 37) shows the point-by-point construction of Euler's line, beginning with the three points of defining the triangle (marked in blue). The circumference O, the centroid G, and the orthocenter H are marked in green, red, and orange, respectively, and the Euler line, in yellow. We call this a construction without words, where the points and lines speak for themselves.

Inverted Circles

Steiner's Prism

Plate 39 illustrates several Steiner chains, each comprising five circles that touch an outer circle (alternately colored in blue and orange) and an inner black circle. The central panel shows this chain in its inverted, symmetric "ball-bearing" configuration.

Line Design

Plate 40.2 shows a Star of David-like design made of 21 line parabolas.

Gothic Rose

Plate 44, Gothic Rose, shows a rosette, a common motif on stained glass windows like those one can find at numerous places of worship. The circle at the center illustrates a fourfold rotation and reflection symmetry, while five of the remaining circles exhibit threefold rotation symmetries with or without reflection (if you disregard the inner details in some of them). The circle in the 10-o'clock position has the twofold rotation symmetry of the yin-yang icon.

Symmetry

Pick's Theorem

Plate 47 shows a lattice polygon with 28 grid points (in red) and 185 interior points (in yellow). Pick's formula gives us the area of this polygon as A = 185 + 28/2 - 1 = 198 square units.

Morley's Theorem

Variations on a Snowflake Curve

Plate 49 is an artistic interpretation of Koch's curve, starting at the center with an equilateral triangle and a hexagram (Star of David) design but approaching the actual curve as we move toward the periphery.

Sierpinski's Triangle

The Rationals Are Countable!

In a way, [Cantor] accomplished the vision of William Blake's famous verse in Auguries of Innocence:

To see the world in a grain of sand,
And heaven in a wild flower.
Hold infinitely in the palm of your hand,
And eternity in an hour.

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Click here to sample selections from the book.