Cryptonomy

Cryptonomy

Fibonacci in crypto: the sequence and how traders use it

Fibonacci tools in technical analysis use mathematical ratios to mark potential support and resistance zones on a price chart. They're based on the Fibonacci sequence, in which each number is the sum of the two before it, but they can't predict the path of a cryptocurrency with certainty.So how did we get from a sequence of numbers to the lines you see on Bitcoin charts? We think Fibonacci is interesting as a tool for organizing your analysis. The problem starts when we ask it to work like a crystal ball.What is the Fibonacci sequenceThe Fibonacci sequence usually starts at 0 and 1 and continues like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… The rule never changes: add the two previous numbers to get the next one.For example, 8 comes from 3 + 5, 13 from 5 + 8 and 21 from 8 + 13. In mathematical notation the rule is written as F(n) = F(n−1) + F(n−2), with starting values F(0) = 0 and F(1) = 1.You'll often see it called the “Fibonacci series.” The more accurate term here is sequence, because we're talking about successive numbers, not their sum. Some presentations start it at 1, 1, which doesn't change the rule.Who was FibonacciFibonacci, also known as Leonardo of Pisa, was an Italian mathematician of the Middle Ages. His work helped spread the Hindu-Arabic numerals and the decimal place-value system in Europe, at a time when calculations were often done in far more cumbersome ways.The sequence became linked to his name through a math problem about breeding rabbits. It wasn't, however, created by a stock market analyst, nor was it designed to predict prices. Similar numerical relationships had been studied even earlier in the Indian mathematical tradition.The golden ratio and Fibonacci ratiosIf you divide a number in the sequence by the one before it, the ratio gradually approaches 1.618…, the golden ratio. For example, 89 / 55 gives roughly 1.618. If you flip the division, the result approaches 0.618, or 61.8%.Related divisions give other ratios too. Dividing a number by the one two places after it approaches 38.2%, while dividing by the one three places after it approaches 23.6%.Fibonacci numbers show up in some plant growth patterns, such as the arrangement of seeds or leaves. That doesn't mean every seashell follows the golden ratio or that planetary orbits are described by the sequence. And above all, the presence of a pattern in nature doesn't prove that a market must follow it.How Fibonacci works in cryptoThe most common application is Fibonacci retracement levels. The analyst picks a completed move between a low and a high, and the tool splits its range into percentage levels.Think of a tape measure that shows how much of the previous rally the price has given back. The tape measures the distance; on its own, it doesn't explain why the market is moving or where it will stop.In an upward move, the levels are used to examine potential support zones during the pullback. In a downward move, they're used for potential resistance zones during the rebound. Support is an area where buying interest may appear, and resistance an area where selling may pick up.Which levels are usedCharting tools usually show 23.6%, 38.2%, 50%, 61.8% and 78.6%, along with the endpoints 0% and 100%. The 78.6% level comes roughly from the square root of 0.618.The 50% level is not a ratio derived from the Fibonacci sequence in the same way. It's included by convention, because a retracement to the halfway point of a move is widely used in technical analysis. The 0% and 100% levels set the boundaries of the measurement.How to draw it on the chartPick the timeframe and a distinct move with a clear start and end.For an upward move, mark the low and then the high. For a downward move, mark the high and then the low.Check which way the percentages run, because the tool's settings can change how they're displayed.Read the levels as areas to watch, not as automatic trading signals.The choice of endpoints changes the result. A daily chart and an hourly chart can produce different zones, and differences also arise if you use candle wicks instead of closing prices. You need a consistent method, not moving the points every time the market disagrees with you.A Fibonacci calculation exampleLet's take a hypothetical example in which Bitcoin moves from 20,000 to 40,000 price units. The numbers are purely for illustration, not current prices or estimates. The range of the rally is 20,000 units.If you measure how far the price pulls back from the high, the calculation is: retracement level = high − (range of the move × retracement percentage).23.6% retracement: 40,000 − 4,720 = 35,280.38.2% retracement: 40,000 − 7,640 = 32,360.50% retracement: 40,000 − 10,000 = 30,000.61.8% retracement: 40,000 − 12,360 = 27,640.This is where people often get confused: a 61.8% retracement from the high is not calculated by adding 61.8% of the range to the low. Before you read any chart, check which end the percentage is measured from.How Fibonacci extensions differRetracement levels look at the pullback within the range of a previous move. Fibonacci extensions project ratios beyond that range, with 161.8% being a common example.Some extension tools use three points: the start of a move, its end and the end of the retracement that followed. These projections describe a hypothetical scenario, not a price the market is bound to reach.Risks and pitfalls in the analysisThe main limitation is that the measurement is subjective. With enough different endpoints and timeframes, you can almost always find some line close to a past reaction. That shows how easily an explanation can be fitted after the fact, not that its predictive value has been proven.A price can cut through level after level without any real reaction. News, thin liquidity or the forced closing of leveraged positions can override any geometric ratio. There's no universal success rate that holds for every cryptocurrency and every period.In practice, analysts often look at previous highs and lows, trading volume and the broader trend together. Even when these line up with a Fibonacci level, their agreement is no guarantee.Our viewThe Cryptonomy team sees Fibonacci as useful as a common language for describing a move. It lets us say how deep a correction was and which areas we're watching, as long as we clearly state the points we measured from and our caveats.For users in Greece, the chart's trading pair matters too: a crypto priced in euros is not the same chart as the same crypto priced in dollars or a stablecoin. Changes in the exchange rate can affect the picture. The mathematical precision of the calculation doesn't mean the prediction is precise.Frequently asked questionsWhat is the Fibonacci system?In technical analysis, it's the use of ratios related to the Fibonacci sequence to map out potential support and resistance zones. On its own, it isn't a complete strategy.What are the first numbers of the Fibonacci sequence?They are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and 55. Each new number equals the sum of the two before it.Why is 61.8% used on charts?It comes from the limit of the ratio of a number in the sequence to the next one, and it's linked to the golden ratio. Its mathematical origin doesn't guarantee that the price will react there.Does Fibonacci work on all cryptocurrencies?It can be drawn on any chart with enough data. How useful it is depends on how it's applied and on market conditions, with no guaranteed result.Does Fibonacci predict whether the price will go up or down?No. It measures the ratios of a chosen move and helps organize possible scenarios. On its own, it doesn't determine the direction of the trend or ensure that a level will hold.

Fibonacci in crypto: the sequence and how traders use it

Crypto books: 5 picks and where to start

If you're looking for books on cryptocurrency, The Basics of Bitcoins and Blockchains is the starting point we recommend for a general introduction, while Mastering Bitcoin suits readers who want technical depth. Below we highlight five titles, explaining what each one offers, where it gets hard and what you shouldn't expect from it.How many times have you read an explanation of Bitcoin and ended up with more questions than you started with? A good book puts the concepts in order, something scattered videos and posts rarely manage. You just need to choose based on what you want to learn, not on how impressive the title sounds.Which crypto book to chooseWanting to understand what a digital wallet does is one thing; wanting to build software for Bitcoin is another. We group the five picks by the reason you're reading:For a general introduction: The Basics of Bitcoins and Blockchains by Antony Lewis.For blockchain without programming: Blockchain Basics by Daniel Drescher.For a technical study of Bitcoin: Mastering Bitcoin by Andreas M. Antonopoulos.For history and storytelling: Bitcoin Billionaires by Ben Mezrich.For applications and the wider economic implications: The Truth Machine by Michael J. Casey and Paul Vigna.We don't treat them as five interchangeable manuals. One explains mechanisms, another tells a story and a third explores possibilities that haven't necessarily materialized. That difference matters more than any ranking of “top” titles.Our 5 picks and what each one offers1. The Basics of Bitcoins and BlockchainsThe Basics of Bitcoins and Blockchains by Antony Lewis is our pick for the reader who first wants to get the basic concepts straight. It connects money, payments, Bitcoin and blockchain, instead of diving straight into difficult technical details.Its strength is a broad introduction that requires no programming. It helps you understand why different cryptocurrencies exist, how the key mechanisms work and what risks come with using them. For a beginner, this big picture is usually more useful than a narrow analysis of a single topic.We wouldn't pick it as a technical manual for building applications. Also, references to services or market practices need checking against newer sources, depending on the edition you have in hand.2. Blockchain BasicsBlockchain Basics: A Non-Technical Introduction in 25 Steps by Daniel Drescher approaches the technology in 25 steps, with no code and no mathematical formulas. It suits people who hear the word blockchain a lot but haven't grasped what problem it's trying to solve.Think of a shared ledger of transactions, with copies kept by different participants. The hard part isn't copying the ledger; it's agreeing which entry is valid when not everyone trusts everyone else. The book's step-by-step approach helps you organize exactly these kinds of concepts.We recommend it for understanding the logic of blockchain, not for instructions on using wallets or evaluating coins. If your main question is “how does this technology work?”, it's a more focused choice than a business story.3. Mastering BitcoinMastering Bitcoin: Programming the Open Blockchain by Andreas M. Antonopoulos is aimed mainly at readers who want to move from description to mechanism. It covers topics such as cryptographic keys, transactions, wallets and the architecture of the peer-to-peer network.Its value lies in the fact that it explains how Bitcoin works at a technical level. If you're a developer or comfortable with technical material, you can use it as a reference book, returning to specific chapters when questions come up.Without the relevant background, the code examples and the details can be tough going. Check the edition carefully: the link above points to a specific older edition and shouldn't be taken as a reference to the latest one. Commands and tools need cross-checking against current documentation.4. Bitcoin BillionairesBitcoin Billionaires by Ben Mezrich follows the Winklevoss twins, from their dispute with Mark Zuckerberg to their involvement with Bitcoin. It's a narrative book, focused on people, conflicts and the business environment.We keep it on the list because the story helps us understand how a community grew around a technology. It reads differently from a manual and can work as a break between more demanding chapters of technical study.Here, though, a clear distinction is needed: a success story is not a recipe for repeating it. The story of specific people doesn't capture all the failures, losses and risks of the same period. We read it as history, not as an investment guide.5. The Truth MachineThe Truth Machine: The Blockchain and the Future of Everything by Michael J. Casey and Paul Vigna widens the discussion beyond Bitcoin. It looks at how blockchain could affect the way data and assets are recorded and exchanged.It suits the reader interested in economics, business and the question of trust. It makes you think about when we need an intermediary and when a shared record-keeping system could reduce that need.The title calls for a critical reading. Blockchain doesn't guarantee that the original data is true: a piece of false information can be recorded just as easily. Also, the possibilities the authors describe should be kept separate from applications that have proven useful in practice.How to check a book before you choose itStart with the table of contents and any available sample. If every other sentence sends you looking up terms, you may need an introductory book first. If you already know the basics, look for specific chapters that answer your questions.Also check the language and the specific edition. The titles here are listed in English; we can't confirm that a Greek translation is available for each of them. Nor does an author's Greek heritage mean their book is published in Greek.Finally, some material ages slowly and some ages fast. The basic principles of cryptography remain useful, but instructions about platforms, apps and regulations may be out of date. A book that promises guaranteed profits makes us more cautious, not more optimistic.What readers in Greece need in additionNone of these titles replaces up-to-date information on Greek tax obligations or the European MiCA regulatory framework. For questions about reporting transactions, you need the current guidance from AADE (Greece's Independent Authority for Public Revenue) and professional advice based on your own situation.You also need separate guidance on security. Your private key, which authorizes transactions, and your seed phrase (recovery phrase), which is used to restore many wallets, must never be shared with anyone. Not even with someone who presents themselves as support and promises to help you put what you've read into practice.Our viewWe think the best starting point for most people is one introductory book followed by a second, more targeted pick. Lewis offers the broadest context, Drescher helps with the logic of blockchain and Mastering Bitcoin opens the door to technical study.Narrative and economics books add perspective, as long as we don't mistake them for proof about the future. For us, a good crypto book is worth it when it helps you ask better questions, not when it gives you certainties about the market.Frequently asked questionsWhich crypto book is suitable for beginners?We recommend The Basics of Bitcoins and Blockchains for a general introduction. If you're mainly interested in how blockchain works without code, Blockchain Basics is more focused.Do I need to know programming?Not for the introductory and narrative books on the list. With Mastering Bitcoin, programming knowledge helps a lot with the technical chapters and the examples.Are these books available in Greek?We can't confirm a Greek edition for every title. Check the language, the publisher and the translator in the bookstore listing before you choose a copy.Is an older Bitcoin book still useful?Yes, for the basic principles and the historical context. Technical instructions, services and legal references need cross-checking against current sources.Can these books tell me which cryptocurrency will go up?No. No book can guarantee future returns. Their value lies in understanding the technology, the history and the risks.

Crypto books: 5 picks and where to start

Crypto and ETF taxation in Greece: a guide for investors

Cryptocurrencies and ETFs often end up in the same portfolio, but in Greece they are taxed under completely different rules. For crypto, Greece has finally got a dedicated law, passed on November 5, 2026. For ETFs, the provisions for securities and mutual funds apply. In this guide we put the two side by side, so you know what you pay in each case. Crypto: the new law From January 1, 2027, crypto gains are taxed at 10%, with a tax-free allowance of up to €500 in net gains a year. Until now, without a specific provision, the prevailing view was that the 15% capital gains tax of Article 42 of the Income Tax Code (KFE) applied. The key rules: Taxable: selling for euros, paying for goods or services with crypto, and contributing crypto to a company. Not taxable: holding crypto, or swapping one crypto for another or for a stablecoin. The cost basis is the average acquisition price of each coin, including fees. If it can’t be proven, it is treated as zero. The tax-free amount is a threshold, not a deduction: with a €501 gain, the whole amount is taxed. Staking and lending are taxed like interest, at 15%. A net loss above €500 can be carried forward for the next 5 years, only against crypto gains. For sales before 2027 there is a voluntary declaration at 10%, with no penalties, within 12 months of the law taking effect. All the details, with examples, are in our guide to crypto taxation. Example Bitcoin purchase (2025)€10,000 Bitcoin sale (2027)€15,000 Gain€5,000 Tax under the new law (10%)€500 Under the old 15% approach€750 The same €5,000 gain from a sale in 2026 is not taxed under the new rules. It can, however, be declared voluntarily at 10%, so that it can be used to justify your deemed-income presumptions (“tekmiria”). With crypto, the tax comes when you cash out to euros. Until then, whatever you swap between coins, you owe nothing. Bitcoin ETFs and ETNs Products that track the price of bitcoin and trade on stock exchanges (ETFs in the US, ETNs and ETPs in Europe) are not crypto-assets. They are financial instruments, so their gains don’t follow the new crypto law but the securities rules described below. The treatment depends on the product’s structure and its country, so it’s a good idea to check with an accountant before you buy. ETFs: the rules ETFs are funds that trade on the stock exchange like shares. They offer cheap diversification across entire markets, such as the 500 largest US companies. But diversification depends on what the ETFs hold, not on their names: in a comparison of 35 popular ETF pairs, SPY, VOO and IVV share more than 99.6% of their holdings. Gains from selling Most ETFs bought by European investors are UCITS, i.e. European mutual funds. Capital gains from selling mutual fund units are exempt from tax under Article 103 of Law 4099/2012, and the prevailing view is that this also covers UCITS ETFs. That doesn’t mean they go undeclared: the sale proceeds are entered on your tax return and help justify purchases and deemed-income presumptions. For non-EU ETFs, such as US ones, the picture is less clear. Their treatment depends on each product’s legal form, so an accountant needs to check it. Besides, most European brokers don’t sell them to retail investors, because of the investor disclosure rules (PRIIPs). Dividends ETFs that pay out dividends (distributing) are taxed in Greece at 5%, like dividends from shares. If tax has already been withheld abroad, it is credited up to the amount of the Greek tax, under the double taxation treaties. ETFs that reinvest dividends (accumulating) don’t pay you a dividend, so there is no tax until you sell. Crypto and ETFs side by side CryptoUCITS ETFs Gains from selling10% from 2027, tax-free up to €500Exempt, according to the prevailing view IncomeStaking, lending: 15%Dividends: 5% LossesAbove €500, for 5 years, only against cryptoIrrelevant, since gains are exempt Reporting to the tax authorityDAC8, from 2026 transactionsCRS, already in force The tax return The Greek tax authority receives data on both. Foreign banks and brokers have been reporting accounts and income through the CRS for years. EU crypto exchanges report transactions from 2026, under the DAC8 directive. The first submission is due by September 30, 2027. For crypto, the new codes on Form E1 haven’t been released yet. They will be set by a decision of AADE (Greece’s Independent Authority for Public Revenue), and we’ll update this guide as soon as they are published. Until then: Keep the statements from every exchange and every broker, for all years. Calculate the average acquisition price for each cryptocurrency. Note the dividends from your ETFs and the tax withheld abroad. Ask an accountant about anything that isn’t UCITS or about crypto sales before 2027. For crypto, the free crypto tax calculator works out the average acquisition price, the gain and the tax for each year from your transactions. This guide was updated on November 7, 2026, after the crypto law was passed, and is not tax advice. For your tax return, consult an accountant. Sources Taxheaven. “The new crypto taxation framework in the bill submitted to Parliament” (in Greek). Accessed November 7, 2026. ot.gr. “Parliament approves a 10% tax on crypto gains” (in Greek). November 5, 2026. Taxheaven. “Income Tax Code (Law 4172/2013)” (in Greek). Taxheaven. “Law 4099/2012, Article 103” (in Greek). Independent Authority for Public Revenue (AADE). “Double taxation treaties”.

Crypto and ETF taxation in Greece: a guide for investors