## Concept explanation A **year** is the time Earth takes to complete one full **orbit** around the Sun. That trip is not exactly `365` days — it is a little longer, about **365.24 days**. This means that after a simple 365-day calendar year, Earth has not quite reached its starting point yet. That leftover fraction is small, but it adds up over time, which is why a calendar based on exactly 365 days is only an approximation. ## What you see You are looking at the Sun in the center and Earth moving around a circular orbit. The gold marker shows where Earth is **after 365 calendar days**, while the teal ring marks where Earth finishes **one full orbit** and returns to the start. The shaded wedge between them shows the small extra part of a day still needed. The cards below summarize the animated day counter, how far around the orbit Earth has gone after 365 days, and the remaining fraction still left. ## Try it yourself - **Drag the year-length slider** between `365.00` and `365.30` days and watch the gold `365 days` marker shift away from the starting point. - **Set the slider to `365.24`** and notice that Earth is very close to the start after 365 days, but not exactly there. - **Move the slider down to `365.00`** to see the gold marker line up with the full-orbit marker, showing what a perfect 365-day year would look like. - **Compare the gold marker and teal full-orbit marker** to see how even a tiny extra fraction creates a visible gap on the orbit. - **Pause the orbit** to study the positions, then **reset the day counter** to replay the motion from the beginning. ## Concept explanation A calendar year is usually treated as `365` days, but Earth actually takes about **365.25 days** to complete one orbit around the Sun. That extra **quarter-day** seems tiny, yet if you ignore it, the **calendar** and Earth’s real **orbital position** slowly slide out of alignment. After about four years, New Year would arrive roughly one full day too early relative to Earth’s place in its orbit, and over longer times that drift would make the **seasons** shift across the calendar. ## What you see Each horizontal row is one year. The blue marker shows where the calendar places **New Year**, while the red marker shows where Earth’s true orbital starting point would be if no leap-day correction were added. The teal line between them is the growing mismatch, and the scale across the top shows the gap in days. As more years are included, you can see the red marker creep farther away from the blue one by about `0.25` day per year. ## Try it yourself - **Drag the years slider** from `1` up to `8` and watch the red orbital marker move farther from the blue calendar marker. - **Stop at year 4** and notice the mismatch is about `1 day`, showing why a correction is needed every four years. - **Press Animate** to see the drift build up smoothly, year by year, instead of jumping straight to the final gap. - **Press Reset** and compare the first year with later years so you can see how a very small yearly error turns into a noticeable seasonal shift. - **Look across the rows** and notice that the gap always grows in the same direction, meaning the calendar would keep slipping earlier relative to Earth’s orbit if nothing corrected it. ## Concept explanation A **calendar year** is usually `365` days, but Earth takes about **365.25 days** to orbit the Sun. That extra quarter-day does not disappear — it **accumulates**. After about four years, those leftover quarters add up to roughly **one full day**, so the calendar inserts a **leap day** to bring the dates back into alignment with Earth’s motion. ## What you see You can compare four years side by side. Each box represents one year of calendar days, while the meter below tracks the leftover quarter-day that builds up after each normal year. As you step forward, one more year becomes active and the meter fills by `1/4`. On the fourth step, the meter reaches about `1 day`, and February in Year 4 gains a `29th` day to show why that year has `366` days. ## Try it yourself - **Click anywhere in the main visual area** to move forward one year and watch the leftover-time meter fill by another quarter-day. - **Press `Add next year`** to step through the same sequence using the control panel. - **Use `Jump to step`** to compare the calendar before any drift has built up, after `1/2` day, and at the full leap-year moment. - **Reset the view** and step through again, noticing that the first three years stay at `365` days while the fourth year adds the extra day. - **Focus on February in Year 4** when the meter is full and notice how the `29th` day appears exactly when enough leftover time has accumulated. ## Concept explanation A **leap year** adds one extra day to the calendar so the year stays aligned with Earth’s orbit around the Sun. That extra day is placed in **February**, which is normally the **shortest month** with `28` days. In a leap year, February alone grows to `29` days, so the whole year changes from `365` to `366` days while every other month stays the same. ## What you see You’re looking at the `12` months as blocks, with each block’s height representing how many days that month has. February is outlined and highlighted so you can spot it as the shortest month right away. The total-day card at the bottom updates with the year length, and when leap year is turned on, only February gains a small extra segment to show exactly where the extra day is inserted. ## Try it yourself - **Click the year toggle** to switch from a normal year to a leap year. - **Watch February carefully** and notice that it changes from `28` to `29` days while the other month blocks stay the same. - **Check the total-day counter** to see the whole year increase from `365` to `366`. - **Click the toggle again** to compare the two calendar versions side by side in your mind. - **Press Reset** to return to the standard calendar and repeat the comparison. ## Concept explanation A **leap year** is a year with one extra day, so it has **366 days** instead of `365`. In the beginner rule shown here, most leap years are easy to spot: if a year is **divisible by 4**, it gets the extra day. That means when a year divides evenly by `4` with **remainder 0**, it follows the leap-year pattern. ## What you see You’re looking at a grid of years from `1996` to `2028`. Leap years are colored differently from normal years, so you can quickly see the repeating every-4-years pattern. When you select a year, the cards below update to show the year’s day count and the result of dividing that year by `4`, including whether the remainder is `0`. ## Try it yourself - **Drag across the year grid** and watch the highlighted year jump from box to box. - **Move the year slider** to scan through the sequence and notice that every fourth year is colored as a leap year. - **Type a year into the input box** and see the day count switch between `365` and `366`. - **Press “Next multiple of 4”** to jump to the next year that divides evenly by `4`. - **Compare nearby years** like `2023` and `2024` to see how the remainder changes from not-evenly-divisible to evenly-divisible. - **Use “Reset to 2024”** to return to a clear leap-year example and confirm that the remainder is `0`. ## Concept explanation A **leap year** usually happens every time a year is divisible by `4`, adding one extra day to February for a total of `366` days. But **century years** such as `1700`, `1800`, and `1900` need a stricter test: they must also be divisible by `400`. This extra rule keeps the calendar from drifting, because adding leap days to every century year would slightly **overcorrect** the match between the calendar and Earth’s actual trip around the Sun. ## What you see You can inspect a set of year cards that all look like good leap-year candidates at first because they are century years and divisible by `4`. Each card shows a badge for whether that year is a leap year or a common year. When you click a card, the inspection panel opens the rule checks step by step and shows a small balance graphic that hints at the idea of the calendar getting too many leap days unless the `÷ 400` rule is used. ## Try it yourself - **Click `1700`, `1800`, and `1900`** and notice that they pass `÷ 4` and `÷ 100` but fail `÷ 400`. - **Click `1600` and `2000`** to see the special century years that do keep their leap day because they are divisible by `400`. - **Use the `Show` dropdown** to focus only on century years or only on leap years. - **Drag the `Card size` slider** to resize the examples and compare the badges more easily. - **Press `Reset focus`** to return to the default view and start inspecting again. ## Concept explanation A **leap year** is a calendar year with **366 days** instead of 365, added to keep our calendar aligned with **Earth’s orbit** around the Sun. The full rule works in layers: if a year is divisible by **4**, it is usually a leap year; if it is also divisible by **100**, that leap day is removed; but if it is divisible by **400**, the leap day is added back. This extra century check matters because Earth’s orbit is about `365.2422` days long, so the complete rule keeps the average calendar year very close to reality over hundreds and thousands of years. ## What you see You’re looking at a decision path with three checkpoints: **÷ 4?**, **÷ 100?**, and **÷ 400?**. As you step forward, the visual highlights the branch your chosen year follows until it reaches a final outcome of `365` or `366` days. The small comparison card below shows why this full rule exists: a simple “every 4 years” pattern would drift over time, while the century and 400-year exceptions keep the long-term average much closer to Earth’s true orbital period. ## Try it yourself - **Enter a year** such as `2024`, `1900`, `2000`, or `2100` to test different cases. - **Press Next step** to walk through the rule one check at a time. - **Press the space bar, `N`, or the right arrow key** to advance without using the mouse. - **Press the left arrow key** to move one step back and reconsider the path. - **Compare `1900` and `2000`** to see why century years need the extra **÷ 400** test. - **Reset the path** and try a non-century year like `2023` or `2024` to see the simpler branch. - **Adjust the animation speed slider** to make the decision path update more slowly or quickly as you step. - **Notice the final `365` or `366` result** and connect it to the orbit comparison below, which shows how the full rule reduces long-term drift.