MediaWiki API result
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See the complete documentation, or the API help for more information.
{
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"logevents": [
{
"logid": 11,
"ns": 6,
"title": "File:Antimetric-pstga.svg",
"pageid": 9,
"logpage": 9,
"revid": 19,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-25T08:53:36Z",
"comment": ""
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"title": "File:Antimetric-pstga.svg",
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"img_timestamp": "2024-11-25T08:53:36Z"
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"type": "upload",
"action": "upload",
"user": "Eric Lengyel",
"timestamp": "2024-11-25T08:53:36Z",
"comment": ""
},
{
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"ns": 6,
"title": "File:Metric-pstga.svg",
"pageid": 8,
"logpage": 8,
"revid": 18,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-25T08:53:23Z",
"comment": ""
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{
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"ns": 6,
"title": "File:Metric-pstga.svg",
"pageid": 8,
"logpage": 8,
"revid": 18,
"params": {
"img_sha1": "m91xws35t20w2m7iej13o1u6z1qfhx8",
"img_timestamp": "2024-11-25T08:53:23Z"
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"type": "upload",
"action": "upload",
"user": "Eric Lengyel",
"timestamp": "2024-11-25T08:53:23Z",
"comment": ""
},
{
"logid": 7,
"ns": 0,
"title": "Metrics",
"pageid": 7,
"logpage": 7,
"revid": 17,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-25T08:50:46Z",
"comment": "Created page with \"The ''metric'' used in the 5D projective geometric algebra over 4D spacetime is the $$5 \\times 5$$ matrix $$\\mathfrak g$$ given by :$$\\mathfrak g = \\begin{bmatrix} -1 & 0 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & 0 \\\\ 0 & 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 0 & 0 \\\\\\end{bmatrix}$$ . The ''metric exomorphism matrix'' $$\\mathbf G$$, often just called the \"metric\" itself, corresponding to the metric $$\\mathfrak g$$ is the $$32 \\times 32$$ matrix shown below. Image:m...\""
},
{
"logid": 6,
"ns": 0,
"title": "Relativistic screw",
"pageid": 6,
"logpage": 6,
"revid": 13,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-24T09:56:56Z",
"comment": "Created page with \"A relativistic screw $$\\mathbf Q$$ is given by :$$\\mathbf Q(2\\tau) = \\exp_\\unicode{x27C7}[\\gamma\\tau(\\dot\\delta\\,\\mathbf e_0 + \\dot\\phi{\\large\\unicode{x1D7D9}}) \\mathbin{\\unicode{x27C7}} \\boldsymbol l - \\gamma c\\tau\\,\\mathbf e_{321}]$$ , where $$c$$ is the speed of light and $$\\gamma = dt/d\\tau$$. The operator $$\\mathbf Q$$ transforms a [[position]] $$\\mathbf r$$ (or any other quantity) through the sandwich product :$$\\mathbf r' = \\mathbf Q \\mathbin{\\unicode{x27C7}}...\""
},
{
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"title": "Translation",
"pageid": 5,
"logpage": 5,
"revid": 12,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-20T01:45:50Z",
"comment": "Created page with \"A spacetime translation operator $$\\mathbf T$$ is given by :$$\\mathbf T(2\\tau) = \\gamma \\dot x\\tau\\,\\mathbf e_{230} + \\gamma \\dot y\\tau\\,\\mathbf e_{310} + \\gamma \\dot z\\tau\\,\\mathbf e_{120} - \\gamma c\\tau\\,\\mathbf e_{321} + {\\large\\unicode{x1D7D9}}$$ . It transforms a [[position]] $$\\mathbf r$$ (or any other quantity) through the sandwich product :$$\\mathbf r' = \\mathbf T \\mathbin{\\unicode{x27C7}} \\mathbf r \\mathbin{\\unicode{x27C7}} \\smash{\\mathbf{\\underset{\\Large\\uni...\""
},
{
"logid": 4,
"ns": 0,
"title": "Velocity",
"pageid": 4,
"logpage": 4,
"revid": 10,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-20T01:24:07Z",
"comment": "Created page with \"The velocity $$\\mathbf u$$ of a body in spacetime is given by :$$\\mathbf u = \\dfrac{d\\mathbf r}{d\\tau} = \\gamma c\\,\\mathbf e_0 + \\gamma \\dot x\\,\\mathbf e_1 + \\gamma \\dot y\\,\\mathbf e_2 + \\gamma \\dot z\\,\\mathbf e_3$$ , where $$\\mathbf r$$ is the body's [[position]] and $$\\tau$$ is proper time. == See Also == * [[Position]] * [[Momentum]]\""
},
{
"logid": 3,
"ns": 0,
"title": "Position",
"pageid": 3,
"logpage": 3,
"revid": 8,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-20T01:20:57Z",
"comment": "Created page with \"The spacetime position $$\\mathbf r$$ of a body is given by :$$\\mathbf r = ct\\,\\mathbf e_0 + x\\,\\mathbf e_1 + y\\,\\mathbf e_2 + z\\,\\mathbf e_3 + \\mathbf e_4$$ . The position $$\\mathbf r$$ has units of length.\""
},
{
"logid": 2,
"ns": 0,
"title": "Momentum",
"pageid": 2,
"logpage": 2,
"revid": 3,
"params": {},
"type": "create",
"action": "create",
"user": "Eric Lengyel",
"timestamp": "2024-11-10T23:49:23Z",
"comment": "Created page with \"The momentum $$\\mathbf P$$ is a bivector quantity with the following ten components. :$$\\mathbf P = m\\mathbf r \\wedge \\dfrac{d\\mathbf r}{d\\tau} = \\gamma m \\left[c \\mathbf e_{40} + \\dot x \\mathbf e_{41} + \\dot y \\mathbf e_{42} + \\dot z \\mathbf e_{43} + (y\\dot z - z\\dot y) \\mathbf e_{23} + (z\\dot x - x\\dot z) \\mathbf e_{31} + (x\\dot y - y\\dot x) \\mathbf e_{12} + c(x - \\dot x t) \\mathbf e_{10} + c(y - \\dot y t) \\mathbf e_{20} + c(z - \\dot z t) \\mathbf e_{30} \\right]$$ ==...\""
}
]
}
}