How to fold an espiral

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I want to make a function that I give it a number and the function returns a spiral from 1 to that number(in 2 dimensional array). For example if I give the number 25 to the function it will return something like this:

I tried different ways but nothing worked out. I just cant figure it out.
Hope I explained myself properly.

4 Answers 4

Mostly the issue here is one of enumerating coordinates – match numbers to coordinates, then print it out however you want.

Start by noticing the two fundamental patterns:

  • (Direction) Move right, then down, then left, then up, then. (this is hopefully obvious)
  • (Magnitude) Move one, then one, then two, then two, then three.

So with those rules, write a generator that yields number, coordinates tuples.

It’s clearest if you set up some helper functions first; I’ll be extra verbose:

Easy enough, now the generator:

How to fold an espiral

Here’s a diagram to help you think about the problem:

How to fold an espiral

You can think of this as repeatedly adding to an NxN square to make an (N+1)x(N+1) square:

and at each step you write a number to the current location.

As @Milan points out, you may not always want to complete the current shell (ie if you only want to count to 23). The easiest way to do this is to make a generator function which produces an endless stream of steps, then consume only as many steps as you need:

Before this can be used we have to decide how to store the values and, based on that, how to represent UP , DOWN , LEFT , and RIGHT .

The simplest storage is a 2d array, or in Python terms a list of lists. The outer list will hold rows of output and the inner lists will each hold cells within a row, and each cell can be addressed as my_array[y][x] with x increasing from left to right and y increasing from the top downward (this matches the order in which we expect to print output).

This allows us to define our directions:

Before we can allocate storage, we need to know how big an array we need:

I have added two extra pieces here: in order for the output to be tidy, every item should print the same width. output() is a function that takes a value and returns a string of the correct width, and EMPTY is a string of spaces of that width:

This geometrical shape isn’t needed frequently, but sometimes, it proves to be very useful.

To draw a spiral, click and drag with the mouse on the canvas. When the left mouse button is released, the spiral will be finished. You will notice two diamond-shaped handles on the spiral.

These handles change the length of the spiral. You can try this out right on the canvas: Just grab one of the handles and drag it along the spiral’s turns to get the desired number of turns and to make the spiral larger or smaller.

If you hold down Ctrl while dragging the handles, the spiral will get longer (or shorter) in 15° steps.

When you combine pressing Alt with pulling the inner handle upwards or downwards, it will change the divergence (tightness) / convergence (looseness) of the spiral, without changing its overall size. Dragging upwards makes the turns move toward the outside of the spiral. Dragging downwards will make them move closer to its center.

The easiest way to change the number of turns of a spiral quickly by a large amount is to enter the desired number into the field labelled Turns in the tool controls bar. This will not change the spiral’s diameter.

If you ever feel lost when working with the spiral tool, you can use the rightmost icon in the tool controls bar to remove all changes and to reset the spiral to its initial shape.

How to fold an espiral

How to fold an espiral

Changing a spiral using its handles.

How to fold an espiral

Alt + dragging the inner handle downwards makes the spiral converge more.

How to fold an espiral

Alt + dragging the inner handle upwards lets the spiral more divergent.

How to fold an espiral

A spiral with a large number of turns.

How to fold an espiral

A spiral with a smaller number of turns.

Meet your new favourite sweet potato recipe! Set in a mesmerising ringed pattern, this Sweet Potato Bake is simple to make, eye-catching and tastes even better than it looks. Here’s an excellent, special occasion-worthy side dish that’s still easy enough for dinner tonight!

How to fold an espiral

A sweet potato side dish to impress!

I actually don’t have that many sweet potato side dishes in my repertoire. I think it’s because when I think of potato side dishes, I tend to think crispy (like Duck Fat Potatoes) or creamy and cheesy (like Potato Dauphinoise). So sweet potatoes are never my natural choice. For one, cream + cheese + sweet potato sounds like an odd combination to me (perhaps someone can prove me wrong here). Secondly, sweet potato just doesn’t properly bake up to be crispy like regular potatoes do.

So I decided it was time to expand my sweet potato collection. This spiral Sweet Potato Bake is what I’ve come up, to put an eye-catching spin on an otherwise straightforward bake!

  • How to fold an espiral
  • How to fold an espiral

What you need to make this Sweet Potato Bake

Here’s what you need to make this dish:

Sweet potatoes – To make this dish look neat, look for long, evenly-shaped ones so the slices will be as similar size as possible. But really, if the sweet potato you find aren’t exactly shaped like the above, don’t let that stop you from making this!

Rosemary – I often pair rosemary with sweet potato. The strong, woody flavour and aroma goes so well, and as a hardy herb it can also stand up to the 50 minutes it takes to bake. Dried herbs would also work here: rosemary, thyme, oregano or a herb mix all come to mind;

Garlic – For flavour. Not many savoury dishes happen around here without garlic!

Butter and oil – Butter for flavour, oil to promote some nice crispy edges.

Did you know? Butter is

20% water and dairy solids. This is enough to stops things from baking up to be crispy. Oil on the other hand is 100% fat and makes things truly crispy. We love butter for flavour, though. So to get the best of both worlds, I use a combination of both!

Salt and pepper

How to make a spiral Sweet Potato Bake

Slice sweet potato – Leave the skin on and slice the potatoes 3-4mm thick. You can make short work of this if you have a mandoline that can slice them to this thickness. We don’t want them too thin or they’ll flop over when you try to arrange them;

Toss – In a large bowl, toss the sweet potato slices with butter, oil, salt, pepper, garlic and rosemary. It’s best to use your hands. Separate the slices as you do this because they tend to stick together. We want each slice nicely coated!

Arrange in skillet – Arrange the sweet potato slices in an ovenproof skillet (mine is 26cm / 11″) in circles. (Yep, you got me, it’s not a true spiral! But rings actually make more sense here to fill the skillet properly.) To do this, gather a stack at a time (photo 3) and place them in the skillet on its side (photo 4). Continue placing end to end until you’re three quarters of the way around the skillet. Then push them over so they overlap each other. As they spread out, they should fill the perimeter of the skillet.

Other shapes: It doesn’t have to be round and it doesn’t have to be a skillet. I used my cast iron skillet because it looks great against the orange potato plus it retains heat so well. You can use a baking dish – round, oval or a 25cm/10″ square one. For square or rectangle dishes, I suggest arranging them in lines rather than spiral;

Arranging in skillet (continued) – As described in step 3 above;

Fill centre – Now do a small overlapping circle in the centre of the skillet, to fill the space as best you can;

Bake covered – Cover with foil and bake for 30 minutes at 180°C/350°F (all oven types). In this step, the potatoes should cook most of the way through but not completely;

Bake uncovered – Remove from the oven then crank up the oven to 220°C/430°F (200°C fan) to brown the top of the potatoes. Remove the foil, drizzle with olive oil (just to give the potatoes a little helping hand for the browning), and pop it back into the oven for 20 minutes or until the tops are a nicely coloured and a bit crispy.

Crispy facts: Sweet potato just doesn’t go truly crispy, unlike regular potato. It’s just a plain fact of life, sadly. We will get some nice edges, but actually they’re more chewy caramelised edges rather than crispy. Still, the caramelised bits are delicious and everyone’s favourite part!

Finally, garnish if desired
with a little sprinkle of fresh, finely chopped rosemary, maybe also a little whole sprig or two, and a pinch of sea salt flakes.

  • How to fold an espiral
  • How to fold an espiral

Now serve your dazzling sweet potato side dish with anything and everything! The only catch is that those edges do soften over time so it’s not the best to keep. As sweet potato already struggles to get real crispiness, it’s at its peak fresh out of the oven. As it cools, the crispy edges soften and they can’t be resurrected.

After leaving it in the fridge overnight, you’ll find it’s completely soft. But that’s not to say it’s not tasty! It still is, with the lovely rosemary-garlic-butter flavour. I’ve been known to give it a freshening by pan-frying slabs of it until golden and crispy. SO GOOD! – Nagi x

Watch how to make it

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Apricot-Rum Glazed Spiral Ham is perfect for the Holidays, and easy since the ham is already cooked you’re basically just heating it up and adding your own glaze.

How to fold an espiralApricot-Rum Glazed Spiral Ham

Ham is perfect to make for the holidays because it’s easy, feeds a lot of people and it’s pretty hard to mess up. Leftovers can be used to make this Leftover Ham Bone Soup with Potatoes and Cabbage, Pressure Cooker Split Pea Soup with Ham and 16 Bean Soup with Ham and Kale.

How to fold an espiral

This recipe was ever so slightly adapted from the cookbook How To Celebrate Everything. An adorable book filled with recipes for Holidays, Family Dinners, Birthday Rituals and everything in between.

Leftover ham is always great in soups, omelets, beans, and fried rice. Really just about anything you want to add flavor to. Since pre-sliced hams are sold fully cooked, all you have to do is warm it through in the oven for about 10 to 12 minutes per pound. If your ham comes with a glaze packet, toss it out and make it with this simple glaze instead. It will taste much better than the questionable ingredients in the packet that comes with the ham.

Swirled with a savory bacon and onion filling, this impressive spiral bread is very good on its own, and makes for an epic sandwich.

How to fold an espiral


  • 12 ounces (340g) sliced bacon
  • 1 1/2 cups (213g) finely diced onions
  • 3 tablespoons (21g) King Arthur Unbleached All-Purpose Flour
  • 1/2 teaspoon black pepper
  • 1 teaspoon paprika
  • 3/4 cup (170g) lukewarm milk
  • 2 tablespoons (28g) water
  • 2 tablespoons (28g) unsalted butter, softened
  • 1 tablespoon (14g) bacon fat (or butter)
  • 1 large egg
  • 2 3/4 cups (330g) King Arthur Unbleached All-Purpose Flour
  • 1/2 cup (57g) King Arthur White Whole Wheat Flour
  • 2 teaspoons instant yeast or active dry yeast
  • 1 teaspoon (6g) salt
  • 2 teaspoons onion powder, optional; for enhanced flavor
  • 1 large egg, beaten with 1 tablespoon water, for brushing on the dough


To make the filling: Cook the bacon until crisp, reserving 2 tablespoons of the fat. Drain the strips on absorbent paper until cool, then finely chop and place in a medium bowl.

Cook the onions in 1 tablespoon of the reserved bacon fat in a heavy skillet set over medium-low heat. Cook, stirring frequently, for 10 to 15 minutes, until the onions are translucent and beginning to brown. Remove from the heat and add the onions to the chopped bacon. Stir in the flour, pepper, and paprika; set aside.

For the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Combine the milk, water, butter, bacon fat, egg, flours, yeast, salt, and onion powder. Mix and knead until the dough is soft and supple; cover and let rise for 1 hour, or until doubled.

After its first rise, pat the dough into an 8″ x 18″ rectangle. Brush with some of the beaten egg mixture, and spread with the bacon filling, leaving 1″ at the short end uncovered. Roll the bread up from the short end toward the uncovered edge, pinching the seam closed. Place seam-side down in a greased 9″ x 5″ loaf pan. Cover loosely with greased plastic wrap and let the dough rise until it domes 1″ above the rim of the pan. While the dough is rising, preheat the oven to 350°F.

Learn more

How to fold an espiral

A better way to make bacon

Brush the top of the risen loaf with the remaining beaten egg mixture. Slash it, and bake for 30 minutes. Tent with foil and bake for an additional 10 to 15 minutes, until the inside of the bread measures 190°F when measured with a digital thermometer.

Remove the bread from the oven and turn it out onto a rack to cool completely before slicing.

How to fold an espiral

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Create Spiral Diagrams in PowerPoint easily. Follow our step by step instruction to draw this useful diagram accurately and quickly.

The spiral model you’ll learn in this tutorial is:

How to fold an espiral

Though the diagram looks simple, it is not so easy to draw this diagram in PowerPoint. In this tutorial you’ll learn to create the diagram in a simple and effective way. But, before that a quick word about…

Spiral life cycle model or Incremental model:

How to fold an espiral

Though the model is quite specific to Software development, the concept is readily applicable in most management and strategic presentations. That is why we thought of giving you step wise instructions on drawing this useful model.

Let us get on with our lesson right away…

1. Draw a set of semicircular arcs

The easiest way to create a spiral diagram is by drawing and merging semi circular arcs.

Go to Auto shapes and select the Arc tool.

How to fold an espiral

Extend the yellow handles till you create a perfect semicircular shape. Test the shape by drawing a flat line and placing the arc on top as shown here:

How to fold an espiral

Getting the arc in a proper semi circular shape is extremely vital for the accuracy of the diagram. Once you get the shape right, make 7 copies of the shape apart from the original one.

Select an arc, go to Format ribbon and enter the height and width as 0.75 each. This will create a semi circular arc with 0.75pt as diameter.

How to fold an espiral

The same way create arcs with diameters of 1.5, 2.25, 3.0, 3.75, 4.5, 5.25 and 6.0pt. Once done, select them all -> Arrange -> Align -> Align Centre and Align Middle. You will get the following result:

How to fold an espiral

2. Group alternative arcs and flip them vertically

The next step is to select alternative arcs and color them red using ‘Shape Outline Color’ option.

How to fold an espiral

Now, group the red and black arcs separately. Select the ‘black arcs’ group -> Arrange -> Rotate -> Flip Vertical. You will get the following result:

How to fold an espiral

Select both the groups -> Arrange -> Align -> Align Right. Change the Shape Outline Weight to 3 pts. Your spiral chart is ready:

How to fold an espiral

You may also be interested in the tutorial for creating a Venn Diagram and see some creative examples of the diagram here >>

Application of the diagram:

You can add an arrow head to the last semi circle of the Spiral Model and place it inside a wheel diagram to indicate spiraling process as follows:

How to fold an espiral

Or you can use the diagram just created as part of segmented wheel like this:

How to fold an espiral

Source: PowerPoint Spirals | CEO Pack 2

You can add an arrow tip at the end of each semi-circle and use the spiral model in a four-quadrant chart as follows:

How to fold an espiral

The application of the diagram is limited only by your imagination.

More Diagram options for business presentations:

Models like the one you learned in this article are essential for any business presenter to communicate their business messages effectively. But, not all business presenters have the time to create these diagrams from the scratch.

That is why we came up with our ‘PowerPoint Graphics, Concepts & Models CEO Pack 2’ – which has 815+ high quality, fully editable PowerPoint templates for busy business presenters like you. Please take a look at some of the samples from the pack:

Circular Cone Diagram

How to fold an espiral

SWOT Analysis Diagram

How to fold an espiral

3D Venn Diagram

How to fold an espiral

You just need to copy the diagrams from the pack to your slides and replace sample text. Your professional presentation gets ready in minutes. It is a smart way to utilize your valuable time.

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Please browse through our templates collection and see how the pack can change the way you create presentation slides forever.

How to fold an espiral

Cut a spiral out of paper as illustrated below. A 6 cm diameter spiral should be sufficient.

Turn on the desk lamp and shine its light towards the ceiling.

Make a whole in the exact centre of the spiral and thread the string through it.

Tie a knot in the end of the string to hold the spiral in place.

Holding the string, dangle the spiral 10 cm above the desk lamp

BE CAREFUL: Don’t let the paper touch the light!

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Why Does This Happen:

The desk lamp light heated the surrounding air. Heating air causes the air molecules to travel farther apart, thereby making the air less dense. Less dense air will always rise above dense air.

As the warm, lighter, air rises upwards the paper spiral begins to spin. The process keeps working because the cooler surrounding air keeps coming towards the light and warming up. This is a simple demonstration of convection currents that exist in thunderstorms and ocean currents. Click here for a simple demonstration of temperature and water density.

Put simply, a convection current is the transfer of heat energy by the movement or flow of a substance from one position to another.

Rain often occurs when an area of warm moist air is forced to rise over a cold air front. This forms a strong convection current of warm moist air moving upwards, known as an updraft. The moisture within the warm air condenses at high altitude, forming cumulus clouds. As the moisture condenses, the water drops become bigger and bigger. Eventually, the water drops within the cloud become too heavy to be held up by the updraft and they start to fall as rain.

Catherine de’ Medici and Elizabeth I also secured some letters with spiral locks.

Jennifer Ouellette – Dec 10, 2021 11:44 pm UTC

How to fold an espiral

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On the eve of her execution for treason in February 1587, Mary, Queen of Scots, penned a letter to King Henri III of France and secured it with a paper lock that featured an intricate spiral mechanism. So-called “letterlocking” was a common practice to protect private letters from prying eyes, but this spiral lock is particularly ingenious and delicate because it incorporates a built-in self-destruct feature, according to a new paper published in the Electronic British Library Journal.

The authors are an interdisciplinary team of researchers working under the umbrella of the Unlocking History Research Group. In this paper, they describe a dozen examples of a spiral lock in letters dated between 1568 and 1638, including one from Mary’s former mother-in-law, Catherine de Medici, as well as her arch-rival, Elizabeth I, who signed Mary’s death warrant.

As we reported previously, co-author Jana Dambrogio, a conservator at MIT Libraries, coined the term “letterlocking” after discovering such letters while a fellow at the Vatican Secret Archives in 2000. The Vatican letters dated back to the 15th and 16th centuries, and they featured strange slits and corners that had been sliced off. Dambrogio realized that the letters had originally been folded in an ingenious manner, essentially “locked” by inserting a slice of the paper into a slit, then sealing it with wax. It would not have been possible to open the letter without ripping that slice of paper—evidence that the letter had been tampered with.

Further Reading

Dambrogio has been studying the practice of letterlocking ever since, often creating her own models to showcase different techniques, eventually forming the Unlocking History Research Group. The practice dates back to the 13th century—at least in Western history—and there are many different folding and locking techniques that emerged over the centuries. “It’s not like people could just go to a shop and buy an envelope,” Dambrogio’s co-author from King’s College London, Daniel Starza Smith, told Ars.

Queen Elizabeth I, Machiavelli, Galileo Galilei, and Marie Antoinette are among the famous personages known to have employed letterlocking for their correspondence. There are hundreds of letterlocking techniques: for example, “butterfly locks,” a simple triangular fold-and-tuck, and an ingenious method known as the “dagger-trap,” which incorporates a booby-trap disguised as another, simpler type of letter lock. And of course, there is the intricate spiral lock that Mary, Queen of Scots, used for her final missive.

How to fold an espiral

Earlier this year, Dambrogio’s team was able to use X-ray tomography to virtually “unlock” a letter written in 1697 by a man named Jacques Sennacque. Their analysis revealed its contents for the first time, right down to the watermark in the shape of a bird, as described in a paper published in the journal Nature Communications. That letter was part of the Brienne Collection, a collection of 2,600 “locked” letters—600 of which had never been opened—found in a 17th-century trunk of undelivered letters preserved in the postal museum at The Hague, the Netherlands.

The unopened letters in the Brienne Collection meant that much more material evidence (crease marks and wax seals, for instance) about a given letter’s internal security was preserved, especially evidence of tucks and layer order, which typically leave no material trace. By contrast, the letters examined in this latest paper have all been opened, presenting a different kind of challenge for the researchers in their ongoing quest to reverse-engineer the creation of letterlocks.

A high percentage of the material evidence for the letterlocks is usually destroyed by opening the letter, and the spiral lock is designed to destroy not just the lock, but also sometimes portions of the actual letter as an added security measure, according to the authors. Subsequent handling by scholars and conservationists can also obscure evidence of the use of a letterlock. Such items are sometimes bound into letter books or stored after flattening and humidification, and the remnants of wax seals might be stored separately, discarded, or reattached incorrectly.