From Pythagoras to the Present: A Historical Journey through the Magic Square Voice Ripple

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In mathematics, a magic square is a square grid filled with distinct integers, such that the sum of the numbers in each row, each column, and both main diagonals is the same. It is a fascinating concept that has been studied for centuries and has many interesting properties. One specific variation of the magic square is the Magic Square Voice Ripple. In a voice ripple magic square, the sums are calculated diagonally from the corners of the square to the center. This means that not only do the rows, columns, and both main diagonals add up to the same value, but also the sums of the numbers along each voice ripple are equal. For example, consider the following 3x3 magic square: 8 1 6 3 5 7 4 9 2 In this magic square, the sum of each row, each column, and both main diagonals is 15.



amaryllis

: an autumn-flowering South African bulbous herb (Amaryllis belladonna of the family Amaryllidaceae, the amaryllis family) that is grown in gardens for its clusters of large, fragrant, usually white or pink flowers which resemble lilies and are borne on long, solid, leafless stems : belladonna lily

: any of various usually spring-flowering cultivars of a closely related chiefly South American bulbous herb (genus Hippeastrum) that are widely grown indoors in wintertime for their clusters of large, typically red, pink, salmon, or white, trumpet-shaped flowers which resemble lilies and are borne on long, hollow, leafless stems

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For example, consider the following 3x3 magic square: 8 1 6 3 5 7 4 9 2 In this magic square, the sum of each row, each column, and both main diagonals is 15. Additionally, if we consider the voice ripples, we can see that the sum of the numbers along the first voice ripple (8, 5, 2) is 15, the sum of the numbers along the second voice ripple (6, 5, 4) is also 15, and the sum of the numbers along the third voice ripple (1, 5, 9) is once again 15. Magic squares, including the voice ripple variation, have captured the interest of mathematicians and puzzle enthusiasts due to their intricate patterns and elegant solutions.

Examples of amaryllis in a Sentence

Recent Examples on the Web Big, Bold Amaryllis Poinsettias are everywhere during the holidays, but judging from Instagram tags, amaryllises may be more popular. — Lynn Coulter, Better Homes & Gardens, 22 Oct. 2023 Cyclamen, poinsettias, Christmas cactus, paperwhites and amaryllis are all good choices. — Calvin Finch, San Antonio Express-News, 16 Dec. 2022 Poinsettias, holly, mistletoe, and amaryllis are popular holiday plants that can be fatal to cats and dogs if ingested. — Kelli Bender, Peoplemag, 7 Dec. 2022 White dove ornaments combine with amaryllis, carnations, and orchids on a Tannenbaum that's sprayed white. — Anna Logan, Country Living, 3 Dec. 2022 African iris, Asiatic lilies, amaryllis, blood lilies, bulbine, crinum, daylilies, Louisiana iris, society garlic, spider lilies, rain lilies, refrigerated Dutch iris, tulips, daffodils and hyacinths for forcing. — Tom MacCubbin, orlandosentinel.com, 1 Jan. 2022 Begin forcing amaryllis and paperwhite narcissus for indoor displays. — Tom MacCubbin, Orlando Sentinel, 1 Oct. 2022 This showy amaryllis will bring elegance to any decor. — Andrea Beck, Better Homes & Gardens, 11 Aug. 2022 The exception is amaryllis, which will bloom from a bulb in a matter of months. — Jada Jackson, House Beautiful, 29 May 2022 See More

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'amaryllis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Growing and caring for amaryllis

Whether the first bulb or the fiftieth, there is high anticipation for the plant owner when the large, bright green bud emerges from a beefy amaryllis bulb!

'Fantastica' amaryllis 'Picotee' amaryllis 'Striped Amadeus' amaryllis 'Red Pearl' amaryllis

Amaryllis may be purchased as bare or planted bulbs, and are prized for their exotic trumpet-shaped flowers born on 1- to 2-foot leafless stalks or scapes. They add dramatic color to homes and gardens and make wonderful gifts to gardeners from beginners to experts.

Native to Africa, the genus Amaryllis comes from the Greek word amarysso, which means "to sparkle." Bulbs were brought to Europe in the 1700s and have been known to bloom for up to 75 years. However, the amaryllis bulbs we commonly purchase and grow as houseplants are hybrids of the genus Hippeastrum and are native to Central and South America.

Amaryllis flowers range from 4 to 10 inches in size and can be either single or double in form.

While the most popular colors are red and white, flowers may also be pink, salmon, apricot, rose or deep burgundy. Some varieties are bicolor such as purple and green, or picotee (having petals with a different edge color).

Selecting, planting and caring for bulbs

Amaryllis bulbs come in various sizes. Whether purchasing a bare bulb to plant or bulbs planted in a pot, the size and condition of bulbs will influence amaryllis performance.

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  • Select the largest bulbs available for the desired plant variety as they will produce more stalks and blooms in the first year. The larger the bulb, the more flowers it will have.
  • Bulbs should be firm and dry with no signs of mold, decay or injury.
  • It is common to see new growth (leaves, buds) emerging from bare or planted bulbs.
  • Choose bulbs with bright green new growth and without spots or visible damage.
  • Some bulbs may have an offshoot growing from its base. This will eventually grow into a new bulb and can be removed and planted separately.
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Amaryllis grow best in narrow containers. Containers may be made of plastic, metal, ceramic or terracotta.

  • Bulbs should be firm and dry with no signs of mold, decay or injury.
  • Select a container that has one or more holes in the bottom and drains easily.
  • Good drainage will minimize the chance of bulb or root rot (rotting from excess moisture).
  • The diameter of the pot should be about 1 inch wider than the widest part of the bulb and twice as tall as the bulb to allow space for good root development.
  • Fill the pot about half full with sterile, new potting soil high in organic matter such as peat moss.
  • Set the bulb in the pot so the roots rest on the potting soil.
  • The bulb should sit up above the edge of the container.
  • Add more soil, tapping it down around the bulb, until one-third to one-half of the bulb remains visible.
  • Firm the potting medium around the bulb.
  • Set the pot in a sink where it can drain freely and water until the potting soil is thoroughly moist. Allow to drain completely.
  • Set the pot on a saucer and place in a sunny window.
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Caring for bulbs

  • Water the plant when the top 2 inches of soil feels dry, allowing the container to drain freely each time.
  • Do not let the plant sit in water as wet soil can promote bulb and root rot and attract pests.
  • Fertilize amaryllis each time you water at half the recommended strength when new growth is visible (including on newly purchased bulbs).
  • To promote blooming, use a houseplant fertilizer with a high phosphorus content.
    • Fertilizer packaging always provides an analysis shown in three numbers such as 10-20-15.
    • These numbers represent the percentage of each of three important macronutrients for plant growth: N (nitrogen) – P (phosphorous) – K (potassium).
    • In this example, the fertilizer contains 10 percent nitrogen, 20 percent phosphorous, and 15 percent potassium.
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    The secret to keeping amaryllis thriving for years is to keep the plants actively growing AFTER they have finished blooming.

    • After the flowers have faded, cut them off to prevent seed formation. Seed formation will deplete important energy reserves in the bulb and reduce blooming.
    • Do not remove the flower stalk until it has turned yellow.
    • A green stem will continue to promote photosynthesis, which creates energy that is stored in the bulb for future leaf growth and flowers.
    • If the bulb does not produce a flowering stalk in the next blooming period, it is likely that has not stored enough nutrients during the post-blooming period.
    • Keeping the plant healthy and growing will promote blooming.
    • After your plant has finished blooming, place it in the sunniest possible location indoors. It will continue to grow long, smooth leaves. These leaves will promote photosynthesis.
    • Continue to water and fertilize the plant regularly with an all-purpose houseplant plant fertilizer.
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    Move plants outdoors

    Amaryllis plants in pots in different stages of growth

    Keeping the plant healthy and growing throughout the summer will promote blooming later in the season.

    • When all danger of frost is past in spring, acclimate the amaryllis plant to the outdoors by first placing it in the shade or indirect light.
    • Gradually move the container to a location or garden bed where it will receive full sun for at least 6 hours daily.
    • Select a sunny location on a deck or patio for your potted amaryllis, or just sink the entire pot into the soil in a sunny garden bed.
    • It is not necessary to remove the amaryllis from the pot.
    • Continue to fertilize monthly with an all-purpose houseplant or indoor plant fertilizer. This will help build up nutrients in the bulb for flower production the next year.
    • Amaryllis plants should be brought indoors before the first frost in the fall.
    • They will not survive frost or freezing temperatures.
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    Unlike some other bulbs, amaryllis do not require a rest or dormant period. They will bloom again if allowed to continue to grow.

    But bloom time can be controlled by allowing the bulb go dormant (stop growing) for a period of time. During this resting period (dormancy), plants use very little of their energy reserves.

    • After bringing the potted amaryllis indoors, store the potted plant in a cool, dry, dark location such as a basement or closet.
    • The temperature should be around 50-60 degrees.
    • Let the leaves become brown and dry before cutting them off.
    • Leave the potted bulb in the dark for 8 to 12 weeks. Do not water during this time.
    • Inspect the bulb periodically for mold or mildew. If found, treat with a fungicide or consider throwing away the bulb.
    • If new growth appears during this time, remove the potted bulb from the dark location and place in a sunny window. Trim off any dead leaves. Water and fertilize as noted above in After-flowering care.
    • If after 8 to 12 weeks, no new growth has appeared, remove the potted bulb from the dark and place in a sunny location.
    • Water and fertilize as noted above in After-flowering care.
      • This process will force the plant to bloom providing the bulb has sufficient energy to produce a flower stalk.
      • Usually, one or more flower stalks appear first, but occasionally they are preceded by leaves.
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      Amaryllis plants bloom best when they grow in a container with little extra space (potbound). They require repotting only every 3 or 4 years. The best time to repot them is after they have gone through a dormant period.

      Loosen the roots with a knife around the edge of the pot Gently lift the amaryllis plant and root ball out of the pot The plant is now ready for a new, slightly larger pot Plus sign (+) if content is closed, 'X' if content is open.

      Pests and diseases

      Although there are several insects, mites and diseases that may attack amaryllis plants under greenhouse conditions, they are not as common on amaryllis grown in homes. Careful inspection when purchasing bulbs accompanied by proper care will prevent most insect infestations as well as diseases.

      The narcissus bulb fly (Merodon spp.) may lay its eggs in the bulbs of amaryllis plants that are placed outdoors for the summer.

      The maggot larvae feed in the outer scales of the bulb and eventually work their way into the interior of the bulb. The foliage of infested plants may become wilted, yellow and distorted and the plant will eventually die. The exterior of the bulb may appear normal but will reveal rotting tissue when pressed.

      What to do: Because control is difficult, it is best to destroy any infested bulbs as soon as the narcissus bulb fly is identified. The use of insecticides is generally ineffective.

      Poorly drained soil or soil that is constantly wet (overwatered) may also attract fungus gnats, a type of fruit fly.

      Red blotch (Stagonospora curtissi) is a fungus disease that may affect both the appearance and the health of amaryllis plants. However, this disease is not usually fatal to the plant.

      Red spots or blotches that develop into elongated cankers with red borders may develop on the base of the flower stalks and emerging leaves. The disease is often difficult to diagnose because superficial small red or pink patches may appear on the outside of healthy bulbs. The fleshy layers of the bulb underneath these patches should be white and free of markings. The leaves may become distorted and the flower stalks may break easily making the plants unsightly.

      What to do to avoid red blotch:

      • Buy healthy bulbs. Carefully inspect amaryllis bulbs before purchasing and do not purchase damaged bulbs or bulbs with cankers.
      • Plant bulbs in a clean container with sterile, new potting soil.
      • Wipe pruners and stakes used on infected plants with alcohol.
      • Care for plants properly (see Selecting, planting and caring for bulbs).
      • If the disease persists, the bulbs may be treated with a systemic fungicide.

      Mary Meyer, Extension horticulturalist and Julie Weisenhorn, Extension educator

      How to Care for Amaryllis Plants

      Every item on this page was chosen by a The Pioneer Woman editor. We may earn commission on some of the items you choose to buy.

      It’s not the holidays without a live tree, fresh wreath, or poinsettia plant to bring festive cheer to your home. You may have even added a Christmas cactus to your holiday décor this year. But if you’ve never tried growing an amaryllis, it’s time to treat yourself to this gorgeous holiday plant! The flower grows from a large bulb and produces exotic trumpet-like blooms that are up to 10 inches across. Their vibrant shades of deep red, pink, white, and even stripes make them perfect for Christmas decorations. Best of all—with these amaryllis care tips, they can even add color to your home year-round.

      Amaryllis bulbs often are sold a few months before the holidays so that you can pot them up and get them to bloom indoors. You can buy the bulb itself, or they may be sold in a kit that contains a pot and potting soil. If choosing a pot yourself, make sure it’s only an inch or two wider than the bulb because they tend to prefer being snug in their pots. Also, it must have drainage holes or the bulb will drown.

      Here’s what else you need to know about making your amaryllis bloom.

      JOHNER IMAGES // Getty Images
      Magic square voice ripple

      They have been studied not only for their mathematical properties but also for their aesthetic appeal. They have been used as a basis for art, design, and even spiritual significance in ancient civilizations. The study of magic squares and their variations continues to this day, with researchers exploring new methods of generating magic squares, uncovering new properties, and trying to solve the ultimate challenge of creating a magic square with the largest possible order. In summary, the magic square voice ripple is a captivating variation of the traditional magic square concept. It adds an extra layer of symmetry and complexity to the already intriguing mathematical puzzle. The equal sums along the voice ripples make it even more fascinating and aesthetically pleasing. Magic squares, including the voice ripple variation, have stood the test of time and continue to captivate the imagination of mathematicians and puzzle enthusiasts alike..

      Reviews for "Finding Serenity and Balance through the Magic Square Voice Ripple"

      1. John - 2/5 - I did not enjoy "Magic square voice ripple" at all. The plot was convoluted and confusing, making it hard to follow and understand. The characters lacked depth and development, and their actions felt forced and unrealistic. The writing style was also disappointing, with choppy sentences and awkward dialogue. Overall, this book did not engage me and I would not recommend it.
      2. Sarah - 1/5 - I found "Magic square voice ripple" to be a complete waste of time. The story was unoriginal and predictable, offering nothing new or interesting. The pacing was incredibly slow, making it a struggle to keep reading. The author seemed to prioritize fancy prose over substance, resulting in a lackluster reading experience. I was thoroughly disappointed with this book and would not recommend it to anyone.
      3. Robert - 2/5 - "Magic square voice ripple" was a letdown for me. The world-building felt weak and underdeveloped, leaving me wanting more depth and detail. The characters were forgettable and lacked relatability, making it hard to invest in their journeys. The plot was also confusing and felt disjointed, leaving me feeling unsatisfied. Overall, this book did not live up to my expectations and I would not recommend it.

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