This is the first in a three-part series on color theory. Warm colors include red, orange, and yellow, and variations of those three colors. These are the colors of fire, of fall leaves, and of sunsets and sunrises, and are generally energizing, passionate, and positive.
Use warm colors in your designs to reflect passion, happiness, enthusiasm, and energy. Red is a very hot color. Red can actually have a physical effect on people, raising blood pressure and respiration rates. Red can be associated with anger, but is also associated with importance think of the red carpet at awards shows and celebrity events. Red also indicates danger the reason stop lights and signs are red, and that warning labels are often red. Outside the western world, red has different associations.
For example, in China, red is the color of prosperity and happiness. It can also be used to attract good luck. In other eastern cultures, red is worn by brides on their wedding days. In South Africa, however, red is the color of mourning. Red is also associated with communism. In design, red can be a powerful accent color. Red can be very versatile, though, with brighter versions being more energetic and darker shades being more powerful and elegant. Orange is a very vibrant and energetic color. In its muted forms it can be associated with the earth and with autumn. Because of its association with the changing seasons, orange can represent change and movement in general.
Orange is also strongly associated with creativity. Because orange is associated with the fruit of the same name, it can be associated with health and vitality. In designs, orange commands attention without being as overpowering as red. Yellow is often considered the brightest and most energizing of the warm colors. Yellow can also be associated with deceit and cowardice, though calling someone yellow is calling them a coward.
Yellow is also associated with hope, as can be seen in some countries when yellow ribbons are displayed by families who have loved ones at war. Yellow is also associated with danger, though not as strongly as red. In some countries, yellow has very different connotations. In Egypt, for example, yellow is for mourning. In your designs, bright yellow can lend a sense of happiness and cheerfulness. Softer yellows are commonly used as a gender-neutral color for babies rather than blue or pink and young children.
Light yellows also give a more calm feeling of happiness than bright yellows. Dark yellows and gold-hued yellows can sometimes look antique and be used in designs where a sense of permanence is desired. Cool colors include green, blue, and purple, are often more subdued than warm colors. They are the colors of night, of water, of nature, and are usually calming, relaxing, and somewhat reserved. Blue is the only primary color within the cool spectrum, which means the other colors are created by combining blue with a warm color yellow for green and red for purple.
Because of this, green takes on some of the attributes of yellow, and purple takes on some of the attributes of red. Use cool colors in your designs to give a sense of calm or professionalism. Each dot only moves out directly from the central stem in a straight line. This process models what happens in nature when the "growing tip" produces seeds in a spiral fashion.
The only active area is the growing tip - the seeds only get bigger once they have appeared. A seed which is i frames "old" still keeps its original angle from the exact centre but will have moved out to a distance which is the square-root of i. It also has a page of links to more resources. Note that you will not always find the Fibonacci numbers in the number of petals or spirals on seed heads etc. Why not grow your own sunflower from seed? I was surprised how easy they are to grow when the one pictured above just appeared in a bowl of bulbs on my patio at home in the North of England.
Perhaps it got there from a bird-seed mix I put out last year? Bird-seed mix often has sunflower seeds in it, so you can pick a few out and put them in a pot. Sow them between April and June and keep them warm. Alternatively, there are now a dazzling array of colours and shapes of sunflowers to try. A good source for your seed is: Nicky's Seeds who supplies the whole range of flower and vegetable seed including sunflower seed in the UK.
Have a look at the online catalogue at Nicky's Seeds where there are lots of pictures of each of the flowers. Which plants show Fibonacci spirals on their flowers? Can you find an example of flowers with 5, 8, 13 or 21 petals? Are there flowers shown with other numbers of petals which are not Fibonacci numbers?
Collect some pine cones for yourself and count the spirals in both directions. A tip: Soak the cones in water so that they close up to make counting the spirals easier.
Are all the cones identical in that the steep spiral the one with most spiral arms goes in the same direction? What about a pineapple? Can you spot the same spiral pattern? How many spirals are there in each direction? From St. Mary's College Maryland USA , Professor Susan Goldstine has a page with really good pine cone pictures showing the actual order of the open "petals" of the cone numbered down the cone.
Fibonacci Statistics in Conifers A Brousseau , The Fibonacci Quarterly vol 7 pages - You will occasionally find pine cones that do not have a Fibonacci number of spirals in one or both directions. Sometimes this is due to deformities produced by disease or pests but sometimes the cones look normal too. This article reports on a study of this question and others in a large collection of Californian pine cones of different kinds. The author also found that there were as many with the steep spiral the one with more arms going to the left as to the right.
On the trail of the California pine , A Brousseau, The Fibonacci Quarterly vol 6 pages pine cones from a large variety of different pine trees in California were examined and all exhibited 5,8 or 13 spirals. Also, many plants show the Fibonacci numbers in the arrangements of the leaves around their stems. If we look down on a plant, the leaves are often arranged so that leaves above do not hide leaves below. This means that each gets a good share of the sunlight and catches the most rain to channel down to the roots as it runs down the leaf to the stem.
Here's a computer-generated image , based on an African violet type of plant, whereas this has lots of leaves. Leaves per turn The Fibonacci numbers occur when counting both the number of times we go around the stem, going from leaf to leaf, as well as counting the leaves we meet until we encounter a leaf directly above the starting one. If we count in the other direction, we get a different number of turns for the same number of leaves. The number of turns in each direction and the number of leaves met are three consecutive Fibonacci numbers! For example, in the top plant in the picture above, we have 3 clockwise rotations before we meet a leaf directly above the first, passing 5 leaves on the way.
If we go anti-clockwise, we need only 2 turns. Notice that 2, 3 and 5 are consecutive Fibonacci numbers. For the lower plant in the picture, we have 5 clockwise rotations passing 8 leaves, or just 3 rotations in the anti-clockwise direction. This time 3, 5 and 8 are consecutive numbers in the Fibonacci sequence.
One estimate is that 90 percent of all plants exhibit this pattern of leaves involving the Fibonacci numbers. Each floret is peaked and is an identical but smaller version of the whole thing and this makes the spirals easy to see. These buttons will show the spirals more clearly for you to count lines are drawn between the florets : Here are some investigations to discover the Fibonacci numbers for yourself in vegetables and fruit.
Take a look at a cauliflower next time you're preparing one: First look at it: Count the number of florets in the spirals on your cauliflower. The number in one direction and in the other will be Fibonacci numbers, as we've seen here. Do you get the same numbers as in the picture? Take a closer look at a single floret break one off near the base of your cauliflower. It is a mini cauliflower with its own little florets all arranged in spirals around a centre. If you can, count the spirals in both directions.
How many are there? Then, when cutting off the florets, try this: start at the bottom and take off the largest floret, cutting it off parallel to the main "stem". Find the next on up the stem. Cut it off in the same way. Repeat, as far as you like and.. Now look at the stem. Where the florets are rather like a pine cone or pineapple. The florets were arranged in spirals up the stem.
Counting them again shows the Fibonacci numbers. Try the same thing for broccoli. Chinese leaves and lettuce are similar but there is no proper stem for the leaves. Instead, carefully take off the leaves, from the outermost first, noticing that they overlap and there is usually only one that is the outermost each time. You should be able to find some Fibonacci number connections.
Look for the Fibonacci numbers in fruit. What about a banana? Count how many "flat" surfaces it is made from - is it 3 or perhaps 5?
Martin, Part II". Besides, he knew what was there. Aegon became the first king of the entire continent of Westeros, save for the southerly region of Dorne. As Gamache journeys further into Quebec, he is drawn deeper into the tortured mind of Peter Morrow, a man so desperate to recapture his fame as an artist that he would sell his soul. As he ran Gamache gripped his rifle and spoke calmly into the headset. More puzzles not in the previous books the first section with some characters from Chaucer's Canterbury Tales and other sections on the Monks of Riddlewell, the squire's Christmas party, the Professors puzzles and so on and all with full solutions of course!
When you've peeled it, cut it in half as if breaking it in half, not lengthwise and look again. There's a Fibonacci number. What about an apple? Instead of cutting it from the stalk to the opposite end where the flower was , i. Try a Sharon fruit. Where else can you find the Fibonacci numbers in fruit and vegetables?
Re:first and ten seasons of passion fall leaves book 1. First and Ten Seasons of Passion Fall Leaves Book 1 and other options as SEASONS OF A SINGLE GIRL . Genius is an American anthology period drama television series developed by Noah Pink and Kenneth Biller which premiered on April 25, on National Geographic. The first season follows the life of Albert Einstein, from his early years, who developed the theory of relativity; the season is based on the book.
Why not email me with your results and the best ones will be put on the Web here or linked to your own web page. Why not measure your friends' hands and gather some statistics? NOTE: When this page was first created back in this was meant as a joke and as something to investigate to show that Phi, a precise ratio of 1. The idea of the lengths of finger parts being in phi ratios was posed in but two later articles investigating this both show this is false. Although the Fibonacci numbers are mentioned in the title of an article in , it is actually about the golden section ratios of bone lengths in the human hand, showing that in hand x-rays only 1 in 12 could reasonably be supposed to have golden section bone-length ratios.
Research by two British doctors in looks at lengths of fingers from their rotation points in almost hands and again fails to find to find phi the actual ratios found were or Radiographic assessment of the relative lengths of the bones of the fingers of the human hand by R. Hamilton and R. However, the 4 petals of the fuchsia really shows there are plants with petals that are definitely not Fibonacci numbers. Four is particularly unusual as the number of petals in plants, with 3 and 5 definitely being much more common. Here are some more examples of non-Fibonacci numbers: Here is a succulent with a clear arrangement of 4 spirals in one direction and 7 in the other: and here is another with 11 and 18 spirals: whereas this Echinocactus Grusonii Inermis has 29 ribs: So it is clear that not all plants show the Fibonacci numbers!
Another common series of numbers in plants are the Lucas Numbers that start off with 2 and 1 and then, just like the Fibonacci numbers, have the rule that the next is the sum of the two previous ones to give: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, , , , , But, no matter what two numbers we begin with, the ratio of two successive numbers in all of these Fibonacci-type sequences always approaches a special value, the golden mean, of 1.
There is more on this and how mathematics has verified that packings based on this number are the most efficient on the next page at this site. In this article two students at the Indian Statistical Institute in Calcutta find that "there is a good deal of variation in the numbers of ray-florets and disc-florets" but the modes most commonly occurring values are indeed Fibonacci numbers. A quote from Coxeter on Phyllotaxis H S M Coxeter, in his Introduction to Geometry , Wiley, page - see the references at the foot of this page - has the following important quote: it should be frankly admitted that in some plants the numbers do not belong to the sequence of f's [Fibonacci numbers] but to the sequence of g's [Lucas numbers] or even to the still more anomalous sequences.
Thus we must face the fact that phyllotaxis is really not a universal law but only a fascinatingly prevalent tendency. Mathematical Mystery Tour by Mark Wahl, , is full of many mathematical investigations, illustrations, diagrams, tricks, facts, notes as well as guides for teachers using the material. It is a great resource for your own investigations. Fascinating Fibonaccis by Trudi Hammel Garland. This is a really excellent book - suitable for all, and especially good for teachers seeking more material to use in class.
Trudy is a teacher in California and has some more information on her book. You can even Buy it online now! She also has published several posters , including one on the golden section suitable for a classroom or your study room wall. Mathematical Models H M Cundy and A P Rollett, third edition, Tarquin, is still a good resource book though it talks mainly about physical models whereas today we might use computer-generated models. Apple cider is a staple of fall, and hard cider kicks the warm, fuzzy feelings up a notch.
When the air begins to turn cool and crisp, cozying up in a blanket with a glass of wine in your hand is pure bliss. The Adirondack Coast Region is ripe with wineries and cideries for you to tour and taste. Fall Attractions for All Elevate your fall Adirondack experience by taking advantage of one, or a few, of the region's exclusive attractions! In the fall, it is a sight to be seen! With lush colors all around and a cool breeze in the air, visitors can spend a fall weekend exploring the Adventure Trail, taking a walking tour to the scenic waterfall, or mountain biking through the trails.
The gift shop is full of local crafts and products, so you can bring a piece of the Adirondacks home with you as well. High Falls Gorge — Looking for a place to see some of the best fall foliage in the Adirondacks? High Falls Gorge is a great day trip spot to capture those oh-so-desired Insta-worthy snapshots. Come see for yourself! Revolution Rail Co. Open weekends through October 28, this unique outdoor experience takes you on a two-hour rail bike tour covering 6 miles of remote railroad tracks through the stunning Adirondack countryside.
Peddle under a canopy of colorful trees, along and over the Hudson River, and visit the historic North Creek Railroad Station. This is a fun, fall activity fitting of your best flannel. Open through the fall, this tree-tops experience gives you a bird's eye view of Adirondack foliage. Stroll the walkways, catch a glimpse from the giant bird's nest, or suspend yourself above the forest floor in a huge spider's web.
It's a fun and educational experience for all ages! When you're done with your walk, head inside to the museum or hit the trails for a hike along the Raquette River. Fort Ticonderoga — Add some history to your fall fun with a trip to Fort Ticonderoga. Get lost in their Heroic Maze and find historic clues to guide you above the towering corn stalks.
Add to the challenge by tackling the maze by moonlight! Meet the animals and then experience their power during live demonstrations.
Local food, wines, and ciders will be available for tasting in the farmer's market, and activities will keep the kids busy all day. Adirondack Experience, the Museum on Blue Mountain Lake — Adirondack Experience takes visitors on a journey through life in the Adirondacks, starting from its earliest settlers and progressing to modern day.
Enjoy traditional pastimes like apple pressing, wagon and pony rides, and square dancing. Make your own seasonal crafts and learn more about fabric arts. Surrounded by the beauty of the Adirondack mountains, and with stunning views of Blue Mountain Lake, it's an authentic Adirondack experience unlike any other. Adirondack Fall Foliage Report. Check back for an up-to-the-minute report on where the leaves are prettiest and most colorful.
Hike to Breathtaking Adirondack Views. The Adirondack Regions. The Adirondack Regions feature over welcoming communities, mountains, lakes, verdant valleys and steep cliffs. Spanning more than six million acres, the Adirondack Mountains are home to the largest protected natural area in the lower 48 of the United States. Like a patchwork quilt, the Adirondacks are made up of twelve distinct regional destinations, each offering their own brand of Adirondack adventure.
From the endless canoeing and kayaking in the Saranac Lake and Tupper Lake regions, to the extensive hiking trails of the High Peaks Wilderness in the Lake Placid Region - discover an area as diverse in geography as it is in activities and events.